The Reconstruction Property in Banach Spaces and a Perturbation Theorem
Canadian mathematical bulletin, Tome 51 (2008) no. 3, pp. 348-358

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Perturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop amore general perturbation theory that does not force equivalence of the sequences.
DOI : 10.4153/CMB-2008-035-3
Mots-clés : 42C15
Casazza, Peter G.; Christensen, Ole. The Reconstruction Property in Banach Spaces and a Perturbation Theorem. Canadian mathematical bulletin, Tome 51 (2008) no. 3, pp. 348-358. doi: 10.4153/CMB-2008-035-3
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[1] [1] Casazza, P. G., Approximation properties. In: Handbook on the Geometry of Banach Spaces. Vol. 1. Elsevier, Amsterdam, 2001, pp. 271–316. Google Scholar

[2] [2] Casazza, P. G., Christensen, O., and Stoeva, D. T., Frame expansions in separable Banach spaces. J. Math. Anal. Appl. 307(2005), no. 2, 710–723. Google Scholar

[3] [3] Christensen, O., A Paley-Wiener theorem for frames. Proc. Amer. Math. Soc. 123(1995), no. 7, 2199–2202. Google Scholar

[4] [4] Diestel, J., Sequences and Series in Banach Spaces. Graduate Texts in Mathematics 92, Springer-Verlag, New York, 1984. Google Scholar

[5] [5] Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces. I. Sequence Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete 92, Springer-Verlag, Berlin, 1977. Google Scholar

[6] [6] Paley, R. E. A. C. and Wiener, N., Fourier transforms in the complex domain. Reprint of the 1934 original. American Mathematical Society Colloquium Publications 19. American Mathematical Society, Providence, RI, 1987. Google Scholar

[7] [7] Singer, I., Bases in Banach Spaces. Die Grundlehren derMathematischen Wissenschaften 154, Springer-Verlag, New York, 1970. Google Scholar

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