Article ID Journal Published Year Pages File Type
4607545 Journal of Approximation Theory 2011 12 Pages PDF
Abstract

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) LpLp or Lp,qLp,q (1≤p<∞1≤p<∞) 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 XX is shrinking (respectively, boundedly complete) if and only if XX does not contain an isomorphic copy of ℓ1ℓ1 (respectively, c0c0).

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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