Banach spaces with the (strong) Gelfand-Phillips property

被引：4

作者：

Banakh, T. ^{[1
,2
]}

Gabriyelyan, S. ^{[3
]}

机构：

[1] Ivan Franko Natl Univ, Lvov, Ukraine

[2] Jan Kochanowski Univ, Kielce, Poland

[3] Ben Gurion Univ Negev, Dept Math, PO 653, Beer Sheva, Israel

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2022年 / 16卷 / 02期

基金：

英国科研创新办公室;

关键词：

Banach space; Gelfand-Phillips property; Strong Gelfand-Phillips property; SUBSPACES;

D O I：

10.1007/s43037-022-00179-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Several new characterizations of the Gelfand-Phillips property are given. We define a strong version of the Gelfand-Phillips property and prove that a Banach space has this stronger property iff it embeds into c(0). For an infinite compact space K, the Banach space C(K) has the strong Gelfand-Phillips property iff C(K) is isomorphic to c(0) iff K is countable and has finite scattered height.

引用

页数：14

共 32 条

[1]

Albiac F, 2006, GRAD TEXTS MATH, V233, P1

[2]

[Anonymous], 2000, Extracta Math

[3]

[Anonymous], 1977, Classical Banach spaces. I. Ergebnisse der Mathematik und ihrer Grenzgebiete

[4]

Banakh, ARXIV211009062

[5]

Bessaga C., 1960, STUD MATH, V19, P53

[6] LIMITED OPERATORS AND STRICT COSINGULARITY [J].

BOURGAIN, J ;

DIESTEL, J .

MATHEMATISCHE NACHRICHTEN, 1984, 119 :55-58

[7] On weak*-extensible Banach spaces [J].

Castillo, Jesus M. F. ;

Gonzalez, Manuel ;

Papini, Pier Luigi .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (13) :4936-4941

[8]

Castillo JMF., 1997, 3 SPACE PROBLEMS BAN, DOI [10.1007/BFb0112511, DOI 10.1007/BFB0112511]

[9] Compact lines and the Sobczyk property [J].

Correa, Claudia ;

Tausk, Daniel V. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (09) :5765-5778

[10] On extensions of c0-valued operators [J].

Correa, Claudia ;

Tausk, Daniel V. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 405 (02) :400-408

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