Weak-star convergence of convex sets

被引：0

作者：

Fitzpatrick, S. ^{[1
]}

Lewis, A. S. ^{[1
]}

机构：

[1] Cornell Univ, ORIE, Ithaca, NY 14853 USA

来源：

JOURNAL OF CONVEX ANALYSIS | 2006年 / 13卷 / 3-4期

关键词：

scalar convergence; weak-star convergence; set convergence; weakly compactly generated;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if a Banach space X is weakly compactly generated and C, C-n are weak-star-closed bounded convex nonempty subsets of the dual space X*, then the support functionals delta(Cn)* n converge to delta(C)* pointwise on X if and only if the sequence (C-n) is uniformly bounded with weak-star limit C.

引用

页码：711 / 719

页数：9

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