Reflexivity, contraction functions and minimum-norm elements

被引：2

作者：

Aizpuru, A ^{[1
]}

García-Pacheco, FJ

机构：

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

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

来源：

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2005年 / 42卷 / 04期

关键词：

minimum-norm element; contraction function; bounded closed convex set;

D O I：

10.1556/SScMath.42.2005.4.7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here we present a new proof of Blatter's result: a normed space is complete if every bounded closed convex subset has an element of minimum norm. We also present geometrical conditions for the existence of minimum-norm elements in bounded closed convex sets. Also, we characterize reflexivity in the class of Banach spaces by means of contraction functions. Furthermore, we study what happens if we remove the completeness hypothesis.

引用

页码：431 / 443

页数：13