On quasi-Chebyshev subspaces of Banach spaces

被引：6
|
作者：
Mohebi, H [2 ]
机构：
[1] Shahid Bahonar Univ Kerman, Dept Math, Kerman, Iran
[2] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada
来源：
JOURNAL OF APPROXIMATION THEORY | 2000年 / 107卷 / 01期
关键词：
Duality; Proximinality; Pseudo-Chebyshev subspace; Quasi-Chebyshev subspace; Reflexive Banach space;
D O I：
10.1006/jath.2000.3483
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A quasi-Chebyshev subspace of a Banach space X has been defined as one in which the set of best approximants for every x in X is non-empty and compact. This generalizes the well known concept of pseudo-Chebyshev property. In this paper we shall give various characterizations of quasi-Chebyshev subspaces in Banach spaces. Moreover, we present a characterization of the spaces in which all closed linear subspaces are quasi-Chebyshev. (C) 2000 Academic Press.
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页码：87 / 95
页数：9
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