Functionals that do not attain their norm

被引：25

作者：

Acosta, Maria D. ^{[1
]}

Aizpuru, Antonio ^{[2
]}

Aron, Richard M. ^{[3
]}

Garcia-Pacheco, Francisco J. ^{[3
]}

机构：

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

[2] Univ Cadiz, Dept Matemat, Cadiz 11510, Spain

[3] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2007年 / 14卷 / 03期

关键词：

norm-attaining functional; non-norm-attaining functional; non-density; density; SETS; LINEABILITY;

D O I：

10.36045/bbms/1190994202

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the set of non-norm-attaining functionals on a Banach space, giving a sufficient condition for the density of this set. We also find a large class of Banach spaces for which the set of norm-attaining functionals is (dense-) lineable. In addition, among other results, we provide a new proof of the fact that every real Banach space can be equivalently renormed so that the set of non-norm-attaining functionals is non-dense.

引用

页码：407 / 418

页数：12

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