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.
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页码：115 / 136
页数：22
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