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Math. 169(1), 667–680 (2020). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs10440-020-00317-x",{"doi":535},"10.1007\u002Fs10440-020-00317-x",{"id":20,"text":537,"url":20,"identifiers":538},"Kuang, J.C.: Applied Inequalities. Shangdong Science and Technology Press, Jinan (2004)",{},{"id":20,"text":540,"url":20,"identifiers":541},"Kuang, J.C.: Real and Functional Analysis, vol. 2. Higher Education Press, Beijing (2015)",{},{"id":20,"text":543,"url":20,"identifiers":544},"Liu, Q.: A Hilbert-type integral inequality under configuring free power and its applications. J. Inequal. Appl. 2019, 91 (2019)",{"doi":545},"10.1186\u002Fs13660-019-2039-1",{"id":20,"text":547,"url":20,"identifiers":548},"Milovanovic, G.V., Rassias, M.T.: Some properties of a hypergeometric function which appear in an approximation problem. J. Glob. Optim. 57, 1173–1192 (2013)",{"doi":549},"10.1007\u002Fs10898-012-0016-z",{"id":20,"text":551,"url":20,"identifiers":552},"Mitrinovi$$\\acute{c}$$, D. S., Pecaric, J. 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Comput. 42, 800–813 (2013)",{},{"id":20,"text":566,"url":20,"identifiers":567},"Rassias, M.T., Yang, B.C.: A Hilbert - type integral inequality in the whole plane related to the hyper geometric function and the beta function. J. Math. Anal. Appl. 428(2), 1286–1308 (2015)",{"doi":568},"10.1016\u002Fj.jmaa.2015.04.003",{"id":20,"text":570,"url":20,"identifiers":571},"Rassias, M.T., Yang, B.C.: Equivalent properties of a Hilbert-type integral inequality with the best constant factor related to the Hurwitz zeta function. Ann. Funct. Anal. 9(2), 282–295 (2018)",{"doi":572},"10.1215\u002F20088752-2017-0031",{"id":20,"text":574,"url":20,"identifiers":575},"Wang, A.Z., Yang, B.C.: A new Hilbert-type integral inequality in whole plane with the non-homogeneous kernel. J. Inequal. Appl. 2011, 123 (2011)",{"doi":576},"10.1186\u002F1029-242X-2011-123",{"id":20,"text":578,"url":20,"identifiers":579},"Xin, D.M.: A Hilbert-type integral inequality with the homogeneous kernel of zero degree. Math. Theory Appl. 30(2), 70–74 (2010)",{},{"id":20,"text":581,"url":20,"identifiers":582},"Xin, D.M., Yang, B.C., Chen, Q.: A discrete Hilbert-type inequality in the whole plane. J. Inequal. Appl. 2016, 133 (2016)",{"doi":583},"10.1186\u002Fs13660-016-1075-3",{"id":20,"text":585,"url":20,"identifiers":586},"Xin, D. M., Yang, B. C.: A Hilbert-type integral inequality in whole plane with the homogeneous kernel of degree -2. J Inequal. Appl. Vol. 2011, Article ID 401428, 11 pages",{"doi":587},"10.1155\u002F2011\u002F401428",{"id":20,"text":589,"url":20,"identifiers":590},"Xu, J.S.: Hardy-Hilbert’s inequalities with two parameters. Adv. Math. 36(2), 63–76 (2007)",{},{"id":20,"text":592,"url":20,"identifiers":593},"Yang, B.C.: On the norm of an integral operator and applications. J. Math. Anal. Appl. 321, 182–192 (2006)",{"doi":594},"10.1016\u002Fj.jmaa.2005.07.071",{"id":20,"text":596,"url":20,"identifiers":597},"Yang, B.C.: A new Hilbert-type integral inequality. Soochow J. Math. 33(4), 849–859 (2007)",{},{"id":20,"text":599,"url":20,"identifiers":600},"Yang, B.C.: A new Hilbert-type integral inequality with some parameters. J. Jilin Univ. (Sci. Ed.) 46(6), 1085–1090 (2008)",{},{"id":20,"text":602,"url":20,"identifiers":603},"Yang, B.C.: A Hilbert-type integral inequality with a non-homogeneous kernel. J. Xiamen Univ. (Nat. Sci.) 48(2), 165–169 (2008)",{},{"id":20,"text":605,"url":20,"identifiers":606},"Yang, B.C.: The Norm of Operator and Hilbert-Type Inequalities. Science Press, Beijing (2009)",{"doi":607},"10.2174\u002F97816080505501090101",{"id":20,"text":609,"url":20,"identifiers":610},"Yang, B.C.: A survey of the study of Hilbert-type inequalities with parameters. Adv. Math. 38(3), 257–268 (2009)",{},{"id":20,"text":612,"url":20,"identifiers":613},"Yang, B.C.: A Hilbert-type integral inequality with the homogenous kernel of degree 0. J. Shandong Univ. (Nat. 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Vol. 2010, Article ID 256796, 9 pages",{"doi":631},"10.1155\u002F2010\u002F256796",{"id":20,"text":633,"url":20,"identifiers":634},"Zeng Z.Z., Raja Rama Gandhi, K., Xie, Z. T.: A new Hilbert-type inequality with the homogeneous kernel of degree -2 and with the integral. Bull. Math. Sci. Appl. 3(1), 11–20 (2014)",{},{"id":20,"text":636,"url":20,"identifiers":637},"Zhao, C.J., Cheung, W.S.: On Hilberts inequalities with alternating signs. J. Math. Inequal. 12(1), 191–200 (2018)",{"doi":638},"10.7153\u002Fjmi-2018-12-15",{"id":20,"text":640,"url":20,"identifiers":641},"Zhao, C.J., Cheung, W.S.: Reverse Hilbert type inequalities. J. Math. Inequal. 13(3), 855–866 (2019)",{"doi":642},"10.7153\u002Fjmi-2019-13-59",{"id":20,"text":644,"url":20,"identifiers":645},"Zhong, J.H., Chen, Q.: A half-discrete Hilbert-type inequality with the decreasing and homogeneous kernel of degree 0 (Chinese). J. Zhejiang Univ. Sci. Ed. 42(1), 77–81 (2015)",{},{"id":647,"createTime":648,"updateTime":649,"relativeEntities":650,"slug":651,"properties":652,"entityType":135,"verifyStatus":136,"verifyTime":663,"verifyNote":138,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":664,"fullTextUrl":20,"authors":665,"publicationType":204,"publisherRelationship":697,"citationCount":166,"citationInfo":752,"publishDate":755,"publishYear":753,"citationAnalyzeStatus":19,"lastCitationAnalyze":756,"indexDatabases":757,"openAccess":20,"references":20,"isForceReanalyzing":332},"b6770bcd-10ff-4564-80a8-7e80d9a787c9","2023-12-22T22:11:54.915+00:00","2026-04-14T16:20:16.200+00:00",[],"Relative-varepsilon-pseudo-weak-demicompactness-and-measures-of-weak-noncompactness",{"abstract":653,"title":655,"gsPaper":657,"references":659,"doi":661},{"EN":654},"In this paper, our central focus is upon a class of linear operators acting on a Banach space X called relatively pseudo weakly demicompact operators. We clarify and determine the relationships with pseudo upper semi-Fredholm and pseudo Fredholm operators. Moreover, a characterization by means of an axiomatic measure of weak noncompactness of linear operators is established. Our results are subsequently used to investigate the relationship between the essential pseudospectrum of the sum of two linear operators and the essential pseudospectrum of each of these operators.",{"EN":656},"Relative $$\\varepsilon$$ -pseudo weak demicompactness and measures of weak noncompactness",{"VOID":658},"[\"18193426789830661866\"]",{"VOID":660},"Akashi, W.Y.: On the perturbation theory for Fredholm operators. Osaka J. Math. 21, 603–612 (1984)\nAmmar, A., Jeribi, A.: A characterization of the essential pseudospectra on a Banach space. J. Arab. Math. 2, 139–145 (2013)\nBanas, J., Rivero, J.: On measures of weak noncompactness. Ann. Mat. 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General Theory, Interscience, New York (1958)\nGoldberg, S.: Unbounded linear operators, theory and applications. McGraw-Hill Book Co., New York (1966)\nJeribi, A.: Linear operators and their essential pseudospectra. Apple Academic Press, Oakville, ON (2018)\nJeribi, A., Krichen, B., Salhi, M.: Characterization of relatively demicompact operators by means of measures of noncompactness. J. Korean Math. Soc. 55, 877–895 (2018)\nKrichen, B.: Relative essential spectra involving relative demicompact unbounded linear operators. Acta Math. Sci. Ser. B Engl. 34, 546–556 (2014)\nKrichen, B., O’Regan, D.: On the class of relatively weakly demicompact nonlinear operators. Fixed Point Theory 19, 625–630 (2018)\nKuratowski C.: Topologie. I. Espaces Métrisables, espaces complets, monografie matematyczne, vol. 20, Warszawa-Wroc law, (1948)\nMüller, V.: Spectral theory of linear operators and spectral systems in Banach algebras. Birkhäuser Verlag, Basel (2003)\nPetryshyn, W.V.: Construction of fixed points of demicompact mappings in Hilbert space. J. Math. Anal. Appl. 14, 276–284 (1966)\nPetryshyn, W.V.: Structure of the fixed points sets of \\(k\\)-set-contractions. Arch. Rational Mech. Anal. 40, 312–328 (1971)\nPetryshyn, W.V.: Remarks on condensing and \\(k\\)-set-contractive mappings. J. Math. Anal. Appl. 39, 717–741 (1972)\nSchechter M.: Principles of functional analysis. Grad. Stud. Math. 36, Am. Math. Soc., Providence, RI, (2002)\nTrefethen, L.N.: Pseudospectra of matrices, numerical analysis. Pitman Res. Notes Math. Ser. 260, 234–266 (1992)\nTrefethen, L.N., Embree, M.: Spectra and pseudospectra. Princeton University Press, Princeton (2005)\nVarah, J.M.: The computation of bounds for the invariant subspaces of a general matrix operator. Stanford University, Stanford (1967)\nWilliams, V.: Closed Fredholm and semi-Fredholm operators, essential spectra and perturbations. J. Funct. Anal. 20, 1–25 (1975)",{"VOID":662},"10.1007\u002Fs43034-020-00100-x","2024-05-06T20:02:38.310+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs43034-020-00100-x",[666,682],{"id":667,"sortIndex":21,"researcher":20,"roles":668,"affiliations":670,"properties":679},"c9c85ff9-3d8b-454e-8448-40f9d52eed74",[669],"AUTHOR",[671],{"id":672,"sortIndex":21,"affiliation":673,"properties":20},"7bd1a1f4-3744-4a65-ac4a-c5e14a922053",{"id":672,"createTime":20,"updateTime":20,"relativeEntities":674,"slug":20,"properties":675,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":678,"statistic":20},[],{"title":676},{"EN":677},"Department of Mathematics, Faculty of Sciences of Sfax; University of Sfax; Sfax Tunisia",[],{"title":680},{"VI":681},"Ines 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báo này đề cập đến vấn đề phép kéo dãn trên các khung Hilbert–Schmidt (HS-frames) (đối khung). Chúng tôi trình bày một định lý kéo dãn từ một khung HS (khung HS Parseval, cặp khung HS đối) tới một cơ sở HS–Riesz (cơ sở HS-orthonormal, cặp cơ sở HS–Riesz đối) và chứng minh rằng khung HS-ortogonal bổ sung tương ứng (khung HS bổ sung chung) là duy nhất với điều kiện tương đương (tương đương đơn vị, tương đương chung). Một ghi chú cũng được cung cấp, cho thấy rằng kết quả và phương pháp của chúng tôi có thể khôi phục một số kết quả kéo dãn hiện có về các khung và g-khung.","This paper addresses the dilation problem on (dual) Hilbert–Schmidt frames (HS-frames). We present a dilation theorem from an HS-frame (a Parseval HS-frame, a dual HS-frame pair) to an HS–Riesz basis (an HS-orthonormal basis, a dual HS–Riesz basis pair); and prove that the corresponding orthogonal complementary HS-frame (joint complementary HS-frame) is unique up to equivalence (unitary equivalence, joint equivalence). A remark is also provided. It demonstrates that our results and approach can recover some existing dilation results on frames and g-frames.",{"EN":769,"VI":770},"Dilations of (dual) Hilbert–Schmidt frames","Phép Kéo Dãn của Các Khung Hilbert–Schmidt (Đối)",{"VOID":772},"[\"6982606954584330927\"]",{"VI":774},"khung Hilbert–Schmidt, phép kéo dãn, cơ sở HS–Riesz, tiên đề Parseval, khung bổ sung, tương đương đơn vị",{"VOID":776},"10.1007\u002Fs43034-022-00181-w","2024-04-28T05:36:24.012+00:00",[779],"VI","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs43034-022-00181-w",[782,797],{"id":783,"sortIndex":21,"researcher":20,"roles":784,"affiliations":785,"properties":794},"ac67548a-b1c3-4e7b-b6bc-ce155308dc70",[669],[786],{"id":787,"sortIndex":21,"affiliation":788,"properties":20},"476764a5-bf33-4bb7-9b52-53b30e2daedd",{"id":787,"createTime":20,"updateTime":20,"relativeEntities":789,"slug":20,"properties":790,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":793,"statistic":20},[],{"title":791},{"VI":792},"Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, People’s Republic of China",[],{"title":795},{"VI":796},"Yun-Zhang Li",{"id":798,"sortIndex":166,"researcher":20,"roles":799,"affiliations":800,"properties":807},"e7fc47da-b7a1-4a45-bf90-e1d27f0f8148",[669],[801],{"id":787,"sortIndex":21,"affiliation":802,"properties":20},{"id":787,"createTime":20,"updateTime":20,"relativeEntities":803,"slug":20,"properties":804,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":806,"statistic":20},[],{"title":805},{"VI":792},[],{"title":808},{"VI":809},"Xiao-Li Zhang",{"url":780,"publisher":811,"properties":861},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":812,"slug":10,"properties":813,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":817,"manageAffiliations":830,"indexDatabases":841,"url":20,"thumbnailPath":20,"statistic":856,"gsStatistic":20,"type":20,"analyzePriority":20},[],{"issn":814,"title":815,"eissn":816},{"VOID":13},{"EN":15},{"VOID":17},[818,822,826],{"id":24,"createTime":20,"updateTime":20,"relativeEntities":819,"label":820,"description":821,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":27},{},{"id":30,"createTime":20,"updateTime":20,"relativeEntities":823,"label":824,"description":825,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":33},{},{"id":36,"createTime":20,"updateTime":20,"relativeEntities":827,"label":828,"description":829,"parentId":20,"standard":20,"scholarHubFieldId":20},[],{"EN":39},{},[831,836],{"id":43,"createTime":20,"updateTime":20,"relativeEntities":832,"slug":20,"properties":833,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":835,"statistic":20},[],{"title":834},{"EN":47},[],{"id":50,"createTime":20,"updateTime":20,"relativeEntities":837,"slug":20,"properties":838,"entityType":20,"verifyStatus":20,"verifyTime":20,"verifyNote":20,"languages":20,"translateLanguages":20,"viewCount":20,"url":20,"parentIds":840,"statistic":20},[],{"title":839},{"EN":54},[56],[842,849],{"id":59,"indexDatabase":843,"url":72,"indexYears":20,"academicFieldIds":848,"indexDatabaseRanking":20},{"id":61,"createTime":20,"updateTime":20,"relativeEntities":844,"label":845,"description":846,"key":68,"publicationTags":847,"standard":20},[],{"EN":64,"VI":64},{"EN":66,"VI":67},[70,71],[74],{"id":76,"indexDatabase":850,"url":87,"indexYears":88,"academicFieldIds":855,"indexDatabaseRanking":93},{"id":78,"createTime":20,"updateTime":20,"relativeEntities":851,"label":852,"description":853,"key":84,"publicationTags":854,"standard":20},[],{"EN":81,"VI":81},{"EN":81,"VI":83},[86],[90,91,92],{"impactFactor":21,"impactFactorByYear":857,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":98,"totalPublicationByYear":858,"totalCitation":104,"totalCitationByYear":859,"totalCitationPerPublication":111,"totalCitationPerPublicationByYear":860,"hindexLast5Year":115,"hindex":115},{"2021":96,"2022":96,"2023":97},{"2019":100,"2020":101,"2021":102,"2022":103,"2023":104,"2024":105},{"2020":107,"2021":108,"2022":109,"2023":110},{"2020":113,"2021":97,"2022":114,"2023":111},{"pages":862,"volume":864},{"VOID":863},"1-20",{"VOID":865},"13",{"total":21,"publishYear":867,"statisticByYear":868},2022,{},"2022-04-26",[93,70],[872,878,881,884,890,893,896,899,902,905,911,914,917,920,923,926,929,932,935,941,944,947,950,953,956,959,962,965,968,971,974,977,980,986,989],{"id":873,"text":874,"url":875,"identifiers":876},"4c68646b-0035-4279-8000-0006b275d4fa","Abdollahi, A., Rahimi, E.: Generalized frames on super Hilbert spaces. Bull. Malays. Math. Sci. Soc. (2) 35(3), 807–818 (2012)","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs10440-022-00541-7",{"doi":877},"10.1007\u002Fs10440-022-00541-7",{"id":873,"text":879,"url":875,"identifiers":880},"Abdollahpour, M.R.: Dilation of dual g-frames to dual g-Riesz bases. Banach J. Math. Anal. 9(1), 54–66 (2015)",{"doi":877},{"id":20,"text":882,"url":20,"identifiers":883},"Aldroubi, A., Cabrelli, C., Molter, U.: Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for \\(L^{2}({\\mathbb{R}}^{d})\\). Appl. Comput. Harmon. Anal. 17(2), 119–140 (2004)",{},{"id":885,"text":886,"url":887,"identifiers":888},"b5bcafa0-fe97-4a09-b788-fa664d8332fd","Arefijamaal, A.A., Sadeghi, G.: von Neumann–Schatten dual frames and their perturbations. Results Math. 69(3–4), 431–441 (2016)","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00025-015-0522-7",{"doi":889},"10.1007\u002Fs00025-015-0522-7",{"id":873,"text":891,"url":875,"identifiers":892},"Arveson, W.: Dilation theory yesterday and today. Oper. Theory Adv. Appl. 207, 99–123 (2010)",{"doi":877},{"id":873,"text":894,"url":875,"identifiers":895},"Asgari, M.S., Khosravi, A.: Frames and bases of subspaces in Hilbert spaces. J. Math. Anal. Appl. 308(2), 541–553 (2005)",{"doi":877},{"id":873,"text":897,"url":875,"identifiers":898},"Bownik, M., Jasper, J., Speegle, D.: Orthonormal dilations of non-tight frames. Proc. Am. Math. Soc. 139(9), 3247–3256 (2011)",{"doi":877},{"id":873,"text":900,"url":875,"identifiers":901},"Casazza, P.G., Han, D., Larson, D.R.: Frames for Banach spaces. Contemp. Math. 247, 149–182 (1999)",{"doi":877},{"id":20,"text":903,"url":20,"identifiers":904},"Casazza, P.G., Kutyniok, G.: Frames of subspaces. Wavelets, frames and operator theory. Contemp. Math. 345, 87–113 (2004)",{},{"id":906,"text":907,"url":908,"identifiers":909},"4a78e1c4-5fc2-4bca-9119-cb3a374206fb","Casazza, P.G., Kutyniok, G., Li, S.: Fusion frames and distributed processing. Appl. Comput. Harmon. Anal. 25(1), 114–132 (2008)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS1063520307001078",{"doi":910},"10.1016\u002Fj.acha.2007.10.001",{"id":20,"text":912,"url":20,"identifiers":913},"Christensen, O.: An Introduction to Frames and Riesz Bases, 2nd edn. Birkhäuser, Basel (2016)",{},{"id":873,"text":915,"url":875,"identifiers":916},"Czaja, W.: Remarks on Naimark’s duality. Proc. Am. Math. Soc. 136(3), 867–871 (2008)",{"doi":877},{"id":873,"text":918,"url":875,"identifiers":919},"Daubechies, I., Grossmann, A., Meyer, Y.: Painless nonorthogonal expansions. J. Math. Phys. 27, 1271–1283 (1986)",{"doi":877},{"id":873,"text":921,"url":875,"identifiers":922},"Dong, J., Li, Y.-Z.: Duality principles in Hilbert–Schmidt frame theory. Math. Methods Appl. Sci. 44(6), 4888–4906 (2021)",{"doi":877},{"id":20,"text":924,"url":20,"identifiers":925},"Dörfler, M., Feichtinger, H.G., Gröchenig, K.: Time-frequency partitions for the Gelfand triple \\((S_{0}, L^{2}, S^{\\prime }_{0})\\). Math. Scand. 98(1), 81–96 (2006)",{},{"id":873,"text":927,"url":875,"identifiers":928},"Duffin, R.J., Schaeffer, A.C.: A class of nonharmonic Fourier series. Trans. Am. Math. Soc. 72, 341–366 (1952)",{"doi":877},{"id":873,"text":930,"url":875,"identifiers":931},"Fornasier, M.: Quasi-orthogonal decompositions of structured frames. J. Math. Anal. Appl. 289(1), 180–199 (2004)",{"doi":877},{"id":873,"text":933,"url":875,"identifiers":934},"Guo, X.: On redundancy, dilations and canonical duals of g-frames in Hilbert spaces. Banach J. Math. Anal. 9(4), 81–99 (2015)",{"doi":877},{"id":936,"text":937,"url":938,"identifiers":939},"e73d90e1-806e-4463-95b0-093f9c3eecc2","Guo, X., Han, D.: Joint similarities and parameterizations for Naimark complementary frames. J. Math. Anal. Appl. 462, 148–156 (2018)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0022247X18301100",{"doi":940},"10.1016\u002Fj.jmaa.2018.01.072",{"id":873,"text":942,"url":875,"identifiers":943},"Guo, X.: Joint similarities and parameterizations for dilations of dual g-frame pairs in Hilbert spaces. Acta Math. Sin. (Engl. Ser.) 35(11), 1827–1840 (2019)",{"doi":877},{"id":873,"text":945,"url":875,"identifiers":946},"Hadwin, D. W.: Dilations and Hahn decompositions for linear maps. Can. J. Math. 33(4), 826–839 (1981)",{"doi":877},{"id":873,"text":948,"url":875,"identifiers":949},"Han, D., Larson, D.: Frames, bases and group representations. Mem. Am. Math. Soc. 147(697), 94 (2000)",{"doi":877},{"id":873,"text":951,"url":875,"identifiers":952},"Han, D., Jing, W., Larson, D., Li, P., Mohapatra, R.N.: Dilation of dual frame pairs in Hilbert \\(C^{*}\\)-modules. Results Math. 63(1–2), 241–250 (2013)",{"doi":877},{"id":873,"text":954,"url":875,"identifiers":955},"Heil, C.: A Basis Theory Primer. Birkhäuser\u002FSpringer, New York (2011)",{"doi":877},{"id":20,"text":957,"url":20,"identifiers":958},"Kashin, B.S., Kulikova, T.Y.: A remark on the description of frames of general form. (Russian) Mat. Zametki 72(6), 941–945 (2002). (translation in Math. Notes 72(5-6), 863–867 (2002))",{},{"id":873,"text":960,"url":875,"identifiers":961},"Li, Y.-N., Li, Y.-Z.: Hilbert–Schmidt frames and their duals. Int. J. Wavelets Multiresolut. Inf. Process. 19(5), 15 (2021). (Paper No. 2150011)",{"doi":877},{"id":873,"text":963,"url":875,"identifiers":964},"Li, S., Ogawa, H.: Pseudoframes for subspaces with applications. J. Fourier Anal. Appl. 10(4), 409–431 (2004)",{"doi":877},{"id":20,"text":966,"url":20,"identifiers":967},"Li, Y.-Z., Zhang, X.-L.: Frame properties of HS-operator sequences. (Submitted)",{},{"id":873,"text":969,"url":875,"identifiers":970},"Najati, A., Faroughi, M.H., Rahimi, A.: g-Frames and stability of g-frames in Hilbert spaces. Methods Funct. Anal. Topol. 14(3), 271–286 (2008)",{"doi":877},{"id":873,"text":972,"url":875,"identifiers":973},"Poria, A.: Approximation of the inverse frame operator and stability of Hilbert–Schmidt frames. Mediterr. J. Math. 14(4), 22 (2017). (Paper No. 153)",{"doi":877},{"id":873,"text":975,"url":875,"identifiers":976},"Sadeghi, G., Arefijamaal, A.: von Neumann–Schatten frames in separable Banach spaces. Mediterr. J. Math. 9(3), 525–535 (2012)",{"doi":877},{"id":873,"text":978,"url":875,"identifiers":979},"Sun, W.: G-frames and g-Riesz bases. J. Math. Anal. Appl. 322(1), 437–452 (2006)",{"doi":877},{"id":981,"text":982,"url":983,"identifiers":984},"27bec44a-de5d-4da0-a638-87673605eac9","Sun, W.: Stability of g-frames. J. Math. Anal. Appl. 326(2), 858–868 (2007)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0022247X06002976",{"doi":985},"10.1016\u002Fj.jmaa.2006.03.043",{"id":873,"text":987,"url":875,"identifiers":988},"Young, R.M.: An Introduction to Nonharmonic Fourier Series. Academic Press, New York (1980)",{"doi":877},{"id":990,"text":991,"url":992,"identifiers":993},"2b1c27f3-fce9-43bf-b304-af0823d7cdb3","Zhu, Y.C.: Characterizations of g-frames and g-Riesz bases in Hilbert spaces. Acta Math. Sin. (Engl. Ser.) 24(10), 1727–1736 (2008)","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs10114-008-6627-0",{"doi":994},"10.1007\u002Fs10114-008-6627-0",{"id":996,"createTime":997,"updateTime":998,"relativeEntities":999,"slug":1000,"properties":1001,"entityType":135,"verifyStatus":136,"verifyTime":1012,"verifyNote":138,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":1013,"fullTextUrl":20,"authors":1014,"publicationType":204,"publisherRelationship":1056,"citationCount":20,"citationInfo":20,"publishDate":1110,"publishYear":867,"citationAnalyzeStatus":1111,"lastCitationAnalyze":998,"indexDatabases":1112,"openAccess":20,"references":20,"isForceReanalyzing":332},"67482060-b79e-4a8d-80ca-e221be2810eb","2023-12-17T19:17:40.360+00:00","2026-03-12T12:50:13.928+00:00",[],"K-frames-for-Krein-spaces",{"abstract":1002,"title":1004,"gsPaper":1006,"references":1008,"doi":1010},{"EN":1003},"The aim of this article is to give a definition of K-frames in Krein spaces. This definition is compatible with K-frames already known in Hilbert spaces and it generalizes them. We will characterize the K-frames by the synthesis operator and the frame operator, likewise to what is seen in the case of Hilbert spaces. In the rest of the article, we will set a definition of dual sequences and some results concerning this notion. Finally, we will demonstrate how to transfer K-frames for Hilbert spaces to Krein spaces arising from a possibly non-regular Gram operator.",{"EN":1005},"K-frames for Krein spaces",{"VOID":1007},"[]",{"VOID":1009},"Azizov, T.Y., Iokhvidov, I.S.: Linear Operators in Spaces with an Indefinite Metric. Wiley, New York (1989)\nBognár, J.: Indefinite Inner Product Spaces, vol. 78. Springer Science and Business Media, Berlin (2012)\nChristensen, O.: An Introduction to Frames and Riesz Bases. Birkhäuser, Boston (2016).. (ISBN 978-3-319-25613-9)\nDaubechies, I., Grossmann, A., Meyer, Y.J.: Painless nonorthogonal expansions. J. Math. Phys. 27(5), 1271–1283 (1986)\nDouglas, G.: On majorization, factorization and range inclusion of operators in Hilbert space. Proc. Am. Math. Soc. 17, 413–416 (1966)\nDuffin, R.J., Schaeffer, A.C.: A class of nonharmonic Fourier series. J. Trans. Am. Math. Soc. 72, 341–366 (1952)\nEsmeral, K., Ferrer, O., Wagner, E.: Frames in Krein spaces arising from a non-regular W-metric. Banach J. Math. Anal. 9(1), 1–16 (2015)\nGăvruta, L.: Frames for operators. Appl. Comput. Harmon. Anal. 32, 139–144 (2012)\nGiribet, J.I., Maestripieri, A., Pería, F.M., Massey, P.G.: On frames for Krein spaces. J. Math. Anal. Appl. 393(1), 122–137 (2012)\nRamu, G., Johnson, P.S.: Frame operators of K-frames. SeMA J. 73(2), 171–181 (2016)\nShamsabadi, M., Arefijamaal, A.: Some results of K-frames and their multipliers. Turk. J. Math. 44, 538–552 (2020)\nXiao X., Zhu, Y.C., Găvruta, L.: Some properties of K-frames in Hilbert spaces. 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Nonlinear Anal. 74, 5844–5850 (2011)\nSadiq Basha, S.: Best proximity points: optimal solutions. J. Optim. Theory Appl. 151, 210–216 (2011)\nSadiq Basha, S.: Best proximity point theorems. J. Approx. Theory 163, 1772–1781 (2011)\nSadiq Basha, S., Shahzad, N.: Best proximity point theorems for generalized proximal contractions. Fixed Point Theory Appl. 2012, 42 (2012)\nSuzuki, T., Kikkawa, M., Vetro, C.: The existence of best proximity points in metric spaces with the property UC. Nonlinear Anal. 71, 2918–2926 (2009)\nWitthayarat, U., Cho, Y.J., Cholamjiak, P.: On solving proximal split feasibility problems and applications. Ann. Funct. Anal. 9, 111–122 (2018)\nWlodarczyk, K., Plebaniak, R., Banach, A.: Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces. 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We prove that every (continuous) \n$${*}$$\n\n-derivable mapping at G from a (unital \n$$C^{*}$$\n\n-algebra) factor von Neumann algebra into its Banach \n$${*}$$\n\n-bimodule is a \n$${*}$$\n\n-derivation if and only if G is a left separating point. A linear mapping \n$$\\delta $$\n\n from a \n$${*}$$\n\n-algebra \n$$\\mathcal {A}$$\n\n into a \n$${*}$$\n\n-left \n$$\\mathcal {A}$$\n\n-module \n$$\\mathcal {M}$$\n\n is a \n$${*}$$\n\n-left derivable mapping at \n$$G\\in \\mathcal {A}$$\n\n if \n$$A\\delta (B)^{*}+B\\delta (A)=\\delta (G)$$\n\n for each A, B in \n$$\\mathcal {A}$$\n\n with \n$$AB^{*}=G$$\n\n. We prove that every continuous \n$${*}$$\n\n-left derivable mapping at a left separating point from a unital \n$$C^{*}$$\n\n-algebra or von Neumann algebra into its Banach \n$${*}$$\n\n-left \n$$\\mathcal {A}$$\n\n-module is identical with zero under certain conditions.",{"EN":1335},"Characterizations of $${*}$$ and $${*}$$ -left derivable mappings on some algebras",{"VOID":1337},"Alaminos, J., Brešar, M., Extremera, J., Villena, A.: Maps preserving zero products. Stud. Math. 193, 131–159 (2009)\nAlaminos, J., Brešar, M., Extremera, J., Villena, A.: Characterizing Jordan maps on \\(C^{*}\\)-algebras through zero products. Proc. Edinb. Math. Soc. 53, 543–555 (2010)\nAlaminos, J., Brešar, M., Extremera, J., Villena, A.: Orthogonality preserving linear maps on group algebras. Math. Proc. Camb. Philos. Soc. 158, 493–504 (2015)\nAn, G., He, J., Li, J.: Characterizing linear mappings through zero products or zero Jordan products, Preprint available at arXiv: 1907.03940v2\nAn, R., Hou, J.: Characterizations of Jordan derivations on rings with idempotent. Linear Multilinear Algebra 58, 753–763 (2010)\nAn, G., Ding, Y., Li, J.: Characterizations of Jordan left derivations on some algebras. Banach J. Math. Anal. 10, 466–481 (2016)\nBrešar, M.: Characterizing homomorphisms, derivations and multipliers in rings with idempotents. Proc. R. Soc. Edinb. Sect. A 137, 9–21 (2007)\nBrešar, M., Vukman, J.: On left derivations and related mappings. Proc. Am. Math. Soc. 110, 7–16 (1990)\nCuntz, J.: On the continuity of Semi-Norms on operator algebras. Math. Ann. 220, 171–183 (1976)\nFadaee, B., Ghahramani, H.: Linear maps behaving like derivations or anti-derivations at orthogonal elements on \\(C^*\\)-algebras, Preprint available at arXiv: 1907.03594v1\nGhahramani, H.: On derivations and Jordan derivations through zero products. Oper. Matrices 8, 759–771 (2014)\nGhahramani, H.: Linear maps on group algebras determined by the action of the derivations or anti-derivations on a set of orthogonal element. Results Math. 73(4), 133 (2018)\nGhahramani, H., Pan, Z.: Linear maps on \\(*\\)-algebras acting on orthogonal element like derivations or anti-derivations. Filomat 13, 4543–4554 (2018)\nGoldstein, S., Paszkiewicz, A.: Linear combinations of projections in von Neumann algebras. Proc. Am. Math. Soc. 116, 175–183 (1992)\nHejazian, S., Niknam, A.: Modules, annihilators and module derivations of \\(JB^{*}\\)-algebras. Indian J. Pure Appl. Math. 27, 129–140 (1996)\nHe, J., Li, J., Qian, W.: Characterizations of centralizers and derivations on some algebras. J. Korean Math. Soc. 54, 685–696 (2017)\nHou, J., An, R.: Additive maps on rings behaving like derivations at idempotent-product elements. J. Pure Appl. Algebra 215, 1852–1862 (2011)\nJiao, M., Hou, J.: Additive maps derivable or Jordan derivable at zero point on nest algebras. Linear Algebra Appl. 432, 2984–2994 (2015)\nJohnson, B.: Symmetric amenability and the nonexistence of Lie and Jordan derivations. Math. Proc. Camb. Philos. Soc. 120, 455–473 (1996)\nKishimoto, A.: Dissipations and derivations. Commun. Math. Phys. 47, 25–32 (1976)\nKoşan, M., Lee, T., Zhou, Y.: Bilinear forms on matrix algebras vanishing on zero products of \\(xy\\) and \\(yx\\). Linear Algebra Appl. 453, 110–124 (2014)\nLi, J., Zhou, J.: Jordan left derivations and some left derivable maps. Oper. Matrices 4, 127–138 (2010)\nLi, J., Zhou, J.: Characterizations of Jordan derivations and Jordan homomorphisms. Linear Multilinear Algebra 59, 193–204 (2011)\nLu, F.: Characterizations of derivations and Jordan derivations on Banach algebras. Linear Algebra Appl. 430, 2233–2239 (2009)\nZhao, S., Zhu, J.: Jordan all-derivable points in the algebra of all upper triangular matrices. Linear Algebra Appl. 433, 1922–1938 (2010)\nZhu, J., Xiong, C.: Derivable mappings at unit operator on nest algebras. 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Springer, Berlin (1991)",{"doi":1611},"10.1007\u002F978-3-642-76724-1",{"id":20,"text":1613,"url":20,"identifiers":1614},"Mujica, J.: Complex Analysis in Banach Spaces, vol. 120. Courier Corporation, North-Holland (1986)",{},{"id":20,"text":1616,"url":20,"identifiers":1617},"Navoyan, K.: Bases in Spaces of Regular Multilinear Operators and Homogeneous Polynomials on Banach Lattices. Doctoral thesis, University of Mississippi (2018)",{},{"id":20,"text":1619,"url":20,"identifiers":1620},"Ryan, R.A.: Applications of Topological Tensor Products to Infinite Dimensional Holomorphy. Doctoral thesis, Trinity College, Dublin (1980)",{},{"id":20,"text":1622,"url":20,"identifiers":1623},"Ryan, R.A.: Introduction to Tensor Products of Banach Spaces. Springer, Berlin (2002)",{"doi":1624},"10.1007\u002F978-1-4471-3903-4",{"id":20,"text":1626,"url":20,"identifiers":1627},"Schep, A.R.: Factorization of positive multilinear maps. IL J. Math. 28, 579–591 (1984)",{},{"id":1629,"createTime":1630,"updateTime":1631,"relativeEntities":1632,"slug":1633,"properties":1634,"entityType":135,"verifyStatus":136,"verifyTime":1631,"verifyNote":138,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":1643,"fullTextUrl":20,"authors":1644,"publicationType":204,"publisherRelationship":1688,"citationCount":20,"citationInfo":20,"publishDate":1743,"publishYear":472,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":1744,"openAccess":20,"references":20,"isForceReanalyzing":332},"b321dbba-43b4-4d04-b3e9-c74b30318374","2023-12-13T03:34:55.800+00:00","2025-02-24T17:50:34.912+00:00",[],"Bounds-for-zeros-of-a-polynomial-using-numerical-radius-of-Hilbert-space-operators",{"abstract":1635,"title":1637,"references":1639,"doi":1641},{"EN":1636},"We obtain bounds for the numerical radius of \n                \n                  \n                \n                $$2 \\times 2$$\n                \n               operator matrices which improve on the existing bounds. We also show that the inequalities obtained here generalize the existing ones. As an application of the results obtained here, we estimate the bounds for the zeros of a monic polynomial and illustrate with numerical examples that the bounds are better than the existing ones.",{"EN":1638},"Bounds for zeros of a polynomial using numerical radius of Hilbert space operators",{"VOID":1640},"Abu-Omar, A., Kittaneh, F.: Generalized spectral radius and norm inequalities for Hilbert space operators, Internat. J. Math. 26(12) (2015) 1550097 9 pp\nAbu-Omar, A., Kittaneh, F.: Estimates for the numerical radius and the spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials. Ann. Funct. Anal. 5(1), 56–62 (2014)\nAl-Dolat, M., Al-Zoubi, K., Ali, M., Bani-Ahmad, F.: General numerical radius inequalities for matrices of operators. Open Math. 14, 109–117 (2016)\nAlpin, Y.A., Chien, M., Yeh, L.: The numerical radius and bounds for zeros of a polynomial. Proc. Amer. Math. Soc. 131, 725–730 (2002)\nBhunia, P., Bag, S., Paul, K.: Numerical radius inequalities and its applications in estimation of zeros of polynomials. Linear Algebra Appl. 573, 166–177 (2019)\nBag, S., Bhunia, P., Paul, K.: Bounds of numerical radius of bounded linear operator using \\(t\\)-Aluthge transform. Math. Inequal. Appl. 23(3), 991–1004 (2020)\nBhunia, P., Paul, K., Nayak, R.K.: On inequalities for A-numerical radius of operators. Electron. J. Linear Algebra 36, 143–157 (2020)\nBhatia, R.: Matrix Analysis. Springer, New York (1997)\nFujii, M., Kubo, F.: Buzano’s inequality and bounds for roots of algebraic equations. Proc. Amer. Math. Soc. 117(2), 359–361 (1993)\nHirzallah, O., Kittaneh, F., Shebrawi, K.: Numerical radius inequalities for certain \\(2\\times 2\\) operator matrices. Integral Equ. Oper. Theory 71, 129–147 (2011)\nHorn, R.A., Johnson, C.R.: Matrix Anallysis. Cambridge University Press, Cambridge (1985)\nKlaja, H., Mashreghi, J., Ransford, T.: On mapping theorems for numerical range. Proc. Am. Math. Soc. 144, 3009–3018 (2016)\nKittaneh, F.: Numerical radius inequalities for Hilbert spaces operators. Stud. Math. 168(1), 73–80 (2005)\nKittaneh, F.: Bounds for the zeros of polynomials from matrix inequalities. Arch. Math. (Basel) 81(5), 601–608 (2003)\nLinden, H.: Bounds for zeros of polynomials using traces and determinants. Seminarberichte Fachbereich Mathematik FeU Hagen. 69, 127–146 (2000)\nPaul, K., Bag, S.: Estimation of bounds for the zeros of a polynomial using numerical radius. Appl. Math. Comput. 222, 231–243 (2013)\nPaul, K., Bag, S.: On the numerical radius of a matrix and estimation of bounds for zeros of a polynomial, Int. J. Math. Math. Sci. 2012 (2012) Article Id 129132 https:\u002F\u002Fdoi.org\u002F10.1155\u002F1012\u002F129132.\nShebrawi, K.: Numerical radius inequalities for certain 2\\(\\times 2\\) operator matrices II. Linear Algebra Appl. 523, 1–12 (2017)\nYamazaki, T.: On upper and lower bounds of the numerical radius and an equality condition. Stud. 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