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Coefficient Quantization in Banach Spaces

S. J. Dilworth·E. Odell·Th. Schlumprecht·Andras Zsak
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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.

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S. J. Dilworth, E. Odell, Th. Schlumprecht, Andras Zsak. 2006-06-13. Coefficient Quantization in Banach Spaces. https://arxiv.org/abs/math/0606317

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