von Neumann–Schatten Dual Frames and their Perturbations
Tóm tắt
In this paper, we discuss the dual of a von Neumann–Schatten p-frames in separable Banach spaces and obtain some of their characterizations. Moreover, we present a classical perturbation result to von Neumann–Schatten p-frames.
Tài liệu tham khảo
Ali S.T., Antoine J.P., Gazeau J.P.: Continuous frames in Hilbert spaces. Ann. Phys. 222, 1–37 (1993)
Arefijamaal A., Sadeghi G.: Frames in 2-inner product spaces. Iran. J. Math. Sci. Inform. 8(2), 123–130 (2013)
Askari-Hemmat A., Dehghan M.A., Radjabalipour M.: Generalized frames and their redundancy. Proc. Am. Math. Soc. 129(4), 1143–1147 (2001)
Askari M.S., Khosravi A.: Frames and bases of subspaces in Hilbert spaces. J. Math. Anal. Appl. 308, 541–553 (2005)
Casazza P.G., Christensen O.: Perturbation of operators and applications to frame theory. J. Fourier Anal. Appl. 5, 543–557 (1997)
Cazassa, P.G., Kutyniok, G.: Frames of subspaces, Contemp. Math., Vol. 345, Am. Math. Soc., Providence, RI, pp. 87–113 (2004)
Cazassa, P.G., Han, D., Larson, D.R.: Frames for Banach spaces, Contemp. Math. Vol. 247, Am. Math. Soc., Providence, RI, (1999), pp. 149–182
Christensen O., Stoeva D.: p-frames in separable Banach spaces. Adv. Comput. Math. 18(2–4), 117–126 (2003)
Christensen O., Eldar Y.C.: Oblique dual frames and shift-invariant spaces. Appl. Comput. Harmon. Anal. 17, 48–68 (2004)
Conway J.B.: A Course in Functional Analysis. Springer, Berlin (1985)
Dörfler M., Feichtinger H.G., Gröchenig K.: Time-frequency partitions for the Gelfand triple \({(S_{0},L^{2}, S^{\prime}_{0})}\) . Math. Scand. 98, 81–96 (2006)
Duffin R.J., Schaeffer A.C.: A class of nonharmonic Fourier series. Trans. Am. Math. Soc. 72, 341–366 (1952)
Gabardo J.P., Han D.: Frames associated with measurable spaces. Adv. Comput. Math. 18(3), 127–147 (2003)
Gröchenig K.: Describing functions: atomic decomposition versus frames. Monatsh. Math. 112, 1–41 (1991)
Li S., Ogawa H.: Pseudoframes for subspaces with applications. J. Fourier Anal. Appl. 10, 409–431 (2004)
Ringrose J.R.: Compact Non-Self-Adjiont Operators. Van Nostrand Reinhold Company, Princeton (1971)
Sadeghi G., Arefijamaal A.: von Neumann–Schatten frames in separable Banach spaces. Mediterr. J. Math. 9, 525–535 (2012)
Sun W.: G-frames and g-Riesz bases. J. Math. Anal. Appl. 322, 437–452 (2006)