期刊
JOURNAL OF APPROXIMATION THEORY
卷 163, 期 5, 页码 640-651出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jat.2011.02.007
关键词
Banach frames; Atomic decompositions; Duality; Reflexivity
类别
资金
- UBACyT [X038, X218]
- CONICET
We study conditions on a Banach frame that ensures the validity of a reconstruction formula. In particular, we show that any Banach frames for (a subspace of) L-p or L-p,L-q (1 <= p < infinity) with respect to a solid sequence space always satisfies an unconditional reconstruction formula. The existence of reconstruction formulas allows us to prove some James-type results for atomic decompositions: an unconditional atomic decomposition (or unconditional Schauder frame) for X is shrinking (respectively, boundedly complete) if and only if X does not contain an isomorphic copy of l(1) (respectively, c(0)). (C) 2011 Elsevier Inc. All rights reserved.
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