Abstract of a paper by Daniel Carando, Silvia Lassalle, and Pablo Schmidberg
This is an announcement for the paper "The reconstruction formula for Banach frames and duality" by Daniel Carando, Silvia Lassalle, and Pablo Schmidberg. 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) $L_p$ or $L_{p,q}$ ($1\le p < \infty$) with respect to a solid sequence space always satisfies an unconditional reconstruction formula. The existence of reconstruction formulae 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 $\ell_1$ (respectively, $c_0$). Archive classification: math.FA math.CA Mathematics Subject Classification: 41A65, 42C15, 46B10, 46B15 Remarks: 16 pages Submitted from: slassall@dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1101.2430 or http://arXiv.org/abs/1101.2430
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alspach@math.okstate.edu