Coefficient Quantization in Banach Spaces
Functional Analysis
2007-05-23 v1
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.
Cite
@article{arxiv.math/0606317,
title = {Coefficient Quantization in Banach Spaces},
author = {S. J. Dilworth and E. Odell and Th. Schlumprecht and Andras Zsak},
journal= {arXiv preprint arXiv:math/0606317},
year = {2007}
}
Comments
LaTeX, 28 pages