Gelfand numbers and widths

被引：13

作者：

Edmunds, David E. ^{[2
]}

Lang, Jan ^{[1
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Univ Sussex, Dept Math, Brighton BN1 9QH, E Sussex, England

来源：

JOURNAL OF APPROXIMATION THEORY | 2013年 / 166卷

关键词：

Gelfand numbers; Gelfand widths; s-numbers; Banach spaces; Compact maps;

D O I：

10.1016/j.jat.2012.10.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In general, the Gelfand widths (c) over tilde (n)(T) of a map T between Banach spaces X and Y are not equivalent to the Gelfand numbers c(n)(T) of T. We show that (c) over tilde (n)(T) = c(n)(T) (n is an element of N) provided that X and Y are uniformly convex and uniformly smooth, and T has trivial kernel and dense range. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：78 / 84

页数：7