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 The source file(s), dosz042106-arXiv.tex: 95960 bytes, is(are) stored in gzipped form as 0606317.gz with size 27kb. The corresponding postcript file has gzipped size 118kb. Submitted from: combs@mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0606317 or http://arXiv.org/abs/math.FA/0606317 or by email in unzipped form by transmitting an empty message with subject line uget 0606317 or in gzipped form by using subject line get 0606317 to: math@arXiv.org.
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Dale Alspach