A characterization of reflexive spaces

被引：6

作者：

Acosta, Maria D. ^{[1
]}

Kadets, Vladimir ^{[2
]}

机构：

[1] Univ Granada, Dept Anal Matemat, E-18071 Granada, Spain

[2] Kharkov Natl Univ, Dept Mech & Math, UA-61077 Kharkov, Ukraine

来源：

MATHEMATISCHE ANNALEN | 2011年 / 349卷 / 03期

关键词：

SET;

D O I：

10.1007/s00208-010-0528-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a Banach space is reflexive if for every equivalent norm, the set of norm attaining functionals has non-empty norm-interior in the dual space. It is also proved that the set of norm attaining functionals on a Banach space that is not a Grothendieck space is not a w*-G (delta) subset of the dual space.

引用

页码：577 / 588

页数：12

共 16 条

[1] On a problem of Namioka on norm-attaining functionals [J].

Acosta, Maria D. ;

Montesinos, Vicente .

MATHEMATISCHE ZEITSCHRIFT, 2007, 256 (02) :295-300

[2] New characterizations of the reflexivity in terms of the set of norm attaining functionals [J].

Acosta, MD ;

Galan, MR .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1998, 41 (03) :279-289

[3] Dual spaces generated by the interior of the set of norm attaining functionals [J].

Acosta, MD ;

Guerrero, JB ;

Galán, MR .

STUDIA MATHEMATICA, 2002, 149 (02) :175-183

[4]

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

[5]

[Anonymous], REND CIRC MAT PALE S

[6]

[Anonymous], 1976, GEOMETRY BANACH SPAC

[7] TOPOLOGICAL PROPERTIES OF THE SET OF NORM-ATTAINING LINEAR FUNCTIONALS [J].

DEBS, G ;

GODEFROY, G ;

SAINTRAYMOND, J .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1995, 47 (02) :318-329

[8]

FABIAN M, 2001, CANAD MATH SOC BOOKS, V8, P129

[9]

Holmes R. B., 1975, Geometric functional analysis and its applications

[10]

James R.C.:., 1964, STUD MATH, V23, P205, DOI [10.4064/sm-23-3-205-216, DOI 10.4064/SM-23-3-205-216]

← 1 2 →