A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers
type: Item
instance of: scholarly article
title: A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers
zbMATH Open document ID: 1017.41025
DOI: 10.1007/BF02638387
published in: Archiv der Mathematik
publication date: 2003-03-27T00:00:00Z
review text: Let \(c_0(X)\) be the space of all null sequences in a Banach space \(X\). It is shown that each compact set in \(c_0(X)\) admits a Chebyshev center if and only if each compact set in \(X\) admits a center. A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers is constructed.
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 46B45
zbMATH DE Number: 1889285
zbMATH Keywords: Banach spaces
zbMATH Keywords: Chebyshev centers
author: Libor Vesely
MaRDI profile type: Publication
cites work: Chebyshev centers and uniform convexity
cites work: Chebyshev centers in normed spaces
cites work: Existence of Chebyshev Centers, Best n-Nets and Best Compact Approximants
cites work: Q3213662
cites work: Geometry of Banach spaces. Selected topics
cites work: On the moduli of convexity and smoothness
cites work: A course on optimization and best approximation
full work available at URL: https://doi.org/10.1007/bf02638387
OpenAlex ID: W2134450424
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description: scientific article; zbMATH DE number 1889285