Characterisations of Chebyshev sets in \(c_{0}\)
type: Item
instance of: scholarly article
title: Characterisations of Chebyshev sets in \(c_{0}\)
zbMATH Open document ID: 1065.41056
published in: Journal of Approximation Theory
publication date: 2004-10-28T00:00:00Z
review text: A subset \(M\) of a normal linear space \(X\) is called a Chebyshev set if there exists a unique best approximation in \(M\) for each \(x\in X\). A characterization of Chebyshev sets which is known for \(l^\infty (n)\) is extended to \(c_0\). A central role play the \textit{coordinate affine subspaces}, i.e. the subspaces of functions which vanish at \(k\) points \((k\in \mathbb N)\) -- and their translations. Two conditions characterize Chebyshev sets. The first one says that the intersections with coordinate affine subspaces are connected. The second one says that locally supporting planes of that kind have an analogous property also globally.
reviewed by: D. Braess
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 2111901
zbMATH Keywords: Chebyshev sets
author: A. R. Alimov
MaRDI profile type: Publication
full work available at URL: j.jat.2004.04.013
OpenAlex ID: W2014818579
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DOI: 10.1016/J.JAT.2004.04.013
description: scientific article; zbMATH DE number 2111901