Structural Properties of Homomorphism Dilation Systems
Tóm tắt
Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, the authors explore a pure algebraic version of the dilation theory for linear systems acting on unital algebras and vector spaces. By introducing two natural dilation structures, namely the canonical and the universal dilation systems, they prove that every linearly minimal dilation is equivalent to a reduced homomorphism dilation of the universal dilation, and all the linearly minimal homomorphism dilations can be classified by the associated reduced subspaces contained in the kernel of synthesis operator for the universal dilation.
Tài liệu tham khảo
citation_title=Dilation theory yesterday and today, A Glimpse at Hilbert Space Operators; citation_inbook_title=Oper. Theory Adv. Appl.; citation_publication_date=2010; citation_pages=99-123; citation_id=CR1; citation_author=W Arveson; citation_publisher=Birkhauser Verlag
citation_journal_title=Contemp. Math.; citation_title=Frames for Banach spaces, The Functional and Harmonic Analysis of Wavelets and Frames (San Antonio, TX, 1999); citation_author=P G Casazza, D G Han, D R Larson; citation_volume=247; citation_publication_date=1999; citation_pages=149-182; citation_doi=10.1090/conm/247/03801; citation_id=CR2
citation_journal_title=Adv. Comput. Math.; citation_title=Frames associated with measurable spaces; citation_author=J P Gabardo, D G Han; citation_volume=18; citation_publication_date=2003; citation_pages=127-147; citation_doi=10.1023/A:1021312429186; citation_id=CR3
citation_journal_title=J. Operator Theory; citation_title=Frame representations for group-like unitary operator systems; citation_author=J P Gabardo, D G Han; citation_volume=49; citation_publication_date=2003; citation_pages=223-244; citation_id=CR4
citation_journal_title=Canad. J. Math.; citation_title=Dilations and Hahn decompositions for linear maps; citation_author=D W Hadwin; citation_volume=33; citation_publication_date=1981; citation_pages=826-839; citation_doi=10.4153/CJM-1981-064-7; citation_id=CR5
citation_journal_title=J. Fourier Anal. Appl.; citation_title=Dilations and completions for Gabor systems; citation_author=D G Han; citation_volume=15; citation_publication_date=2009; citation_pages=201-217; citation_doi=10.1007/s00041-008-9028-y; citation_id=CR6
citation_journal_title=Mem. Amer. Math. Soc.; citation_title=Frames, bases and group representations; citation_author=D G Han, D R Larson; citation_volume=697; citation_publication_date=2000; citation_pages=1-94; citation_id=CR7
Han, D. G., Larson, D. R., Liu, B. and Liu, R., Operator-valued measures, dilations, and the theory of frames, Mem. Amer. Math. Soc., 229(1075), 2014.
citation_journal_title=J. Funct. Anal.; citation_title=Dilations for systems of imprmimitivity acting on Banach spaces; citation_author=D G Han, D R Larson, B Liu, R Liu; citation_volume=266; citation_publication_date=2014; citation_pages=6914-6937; citation_doi=10.1016/j.jfa.2014.02.040; citation_id=CR9
citation_title=Dilations of Frames, Operator Valued Measures and Bounded Linear Maps; citation_inbook_title=Contemp. Math.; citation_publication_date=2014; citation_pages=33-53; citation_id=CR10; citation_author=D G Han; citation_author=D R Larson; citation_author=B Liu; citation_author=R Liu; citation_publisher=Amer. Math. Soc.
citation_journal_title=J. Funct. Anal.; citation_title=Dilations of operator-valued measures with bounded p-variations and framings on Banach spaces; citation_author=D G Han, D R Larson, R Liu; citation_volume=274; citation_publication_date=2018; citation_pages=1466-1490; citation_doi=10.1016/j.jfa.2018.01.006; citation_id=CR11
citation_journal_title=Amer. J. Math.; citation_title=On the orthogonalization of operator representations; citation_author=R Kadison; citation_volume=77; citation_publication_date=1955; citation_pages=600-622; citation_doi=10.2307/2372645; citation_id=CR12
citation_journal_title=Izv. Akad. Nauk SSSR Ser. Mat.; citation_title=Spectral functions of a symmetric operator; citation_author=M A Naimark; citation_volume=4; citation_publication_date=1940; citation_pages=277-318; citation_id=CR13
citation_journal_title=Dokl. Acad. Sci. SSSR; citation_title=On a representation of additive operator set functions; citation_author=M A Naimark; citation_volume=41; citation_publication_date=1943; citation_pages=373-375; citation_id=CR14
citation_title=Completely Bounded Maps and Operator Algebras; citation_publication_date=2002; citation_id=CR15; citation_author=V Paulsen; citation_publisher=Cambridge University Press
citation_journal_title=Proc. Amer. Math. Soc.; citation_title=Positive functions on C*-algebras; citation_author=W F Stinespring; citation_volume=6; citation_publication_date=1955; citation_pages=211-216; citation_id=CR16