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
收藏
页码：87 / 95
页数：9
相关论文
共 50 条
  • [21] The Hahn-Banach subspaces of Banach spaces with base
    Kubzdela, A
    [J]. ULTRAMETRIC FUNCTIONAL ANALYSIS, 2003, 319 : 179 - 189
  • [22] BALL REMOTAL SUBSPACES OF BANACH SPACES
    Bandyopadhyay, Pradipta
    Lin, Bor-Luh
    Rao, T. S. S. R. K.
    [J]. COLLOQUIUM MATHEMATICUM, 2009, 114 (01) : 119 - 133
  • [23] Complemented subspaces of products of Banach spaces
    Chigogidze, A
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (10) : 2959 - 2963
  • [24] Banach spaces without minimal subspaces
    Ferenczi, Valentin
    Rosendal, Christian
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 257 (01) : 149 - 193
  • [25] ON SUBSPACES OF BANACH SPACES WITHOUT QUASICOMPLEMENTS
    LINDENSTRAUSS, J
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 1968, 6 (01) : 36 - +
  • [26] On quasicomplemented Hilbertian subspaces of Banach spaces
    Plichko, Anatolij
    Sobchuk, Oleksandr
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 500 (01)
  • [27] On Weak*-Extensible Subspaces of Banach Spaces
    Martinez-Cervantes, G.
    Rodriguez, J.
    [J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (02)
  • [28] Orthogonally complemented subspaces in Banach spaces
    Hudzik, Henryk
    Wang, Yuwen
    Sha, Ruli
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) : E1701 - E1711
  • [29] Almost constrained subspaces of Banach spaces
    Bandyopadhyay, P
    Dutta, S
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (01) : 107 - 115
  • [30] ABSOLUTE SUBSPACES OF BANACH-SPACES
    MENAJURADO, JF
    PAYAALBERT, R
    RODRIGUEZPALACIOS, A
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 1989, 40 (157): : 43 - 64
12345