[Banach] Abstract of a paper by S. J. Dilworth, E. Odell, Th. Schlumprecht, and Andras Zsak

This is an announcement for the paper "Coefficient quantization in Banach spaces" by S. J. Dilworth, E. Odell, Th. Schlumprecht, and Andras Zsak.

Abstract: Let (e_i) be a dictionary for a separable Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a `finite alphabet'. We investigate several approximation properties of this type and connect them to the Banach space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c_0.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B20; 41A65

Remarks: LaTeX, 28 pages

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Submitted from: combs@mail.ma.utexas.edu

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