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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