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.

引用

页码：87 / 95

页数：9

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