REMOTALITY OF CLOSED BOUNDED CONVEX SETS IN REFLEXIVE SPACES

被引：14

作者：

Sababheh, M. ^{[2
]}

Khalil, R. ^{[1
]}

机构：

[1] Univ Jordan, Dept Math, Amman 11942, Jordan

[2] Princess Sumaya Univ Technol, Dept Sci & Humanities, Amman, Jordan

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2008年 / 29卷 / 9-10期

关键词：

Approximation theory in Banach spaces; Remotal sets;

D O I：

10.1080/01630560802458033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a Banach space and E be a closed bounded subset of X. For x is an element of X, we define D(x, E) = sup {parallel to x - e parallel to : e is an element of E}. The set E is said to be remotal (in X) if, for every x is an element of X, there exists epsilon is an element of E such that D(x, E) = parallel to x - e parallel to. The object of this paper is to characterize those reflexive Banach spaces in which every closed bounded convex set is remotal. Such a result enabled us to produce a convex closed and bounded set in a uniformly convex Banach space that is not remotal. Further, we characterize Banach spaces in which every bounded closed set is remotal.

引用

页码：1166 / 1170

页数：5