Norm Attaining Operators and Pseudospectrum

被引：12

作者：

Shkarin, S. ^{[1
]}

机构：

[1] Queens Univ Belfast, Dept Pure Math, Belfast BT7 1NN, Antrim, North Ireland

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2009年 / 64卷 / 01期

关键词：

Norm of the resolvent; pseudospectrum; norm attaining operators; CLASSICAL BANACH-SPACES; CONVEX-SPACES; DENSENESS;

D O I：

10.1007/s00020-009-1676-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that if 1 < p < infinity and X is a subspace or a quotient of an l(p)-direct sum of finite dimensional Banach spaces, then for any compact operator T on X such that parallel to I + Tk parallel to > 1, the operator I + T attains its norm. A reflexive Banach space X and a bounded rank one operator T on X are constructed such that parallel to I + Tk parallel to > 1 and I + T does not attain its norm.

引用

页码：115 / 136

页数：22

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