Norm attaining operators and pseudospectrum

Stanislav Shkarin

Norm attaining operators and pseudospectrum

Research output: Contribution to journal › Article › peer-review

Abstract

It is shown that if $11$, 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 $\|I+T\|>1$ and $I+T$ does not attain its norm.

Original language	English
Pages (from-to)	115-136
Number of pages	22
Journal	Integral Equations and Operator Theory
Volume	64
Issue number	1
Publication status	Published - May 2009

ASJC Scopus subject areas

Algebra and Number Theory
Analysis

Cite this

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title = "Norm attaining operators and pseudospectrum",

abstract = "It is shown that if $11$, 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 $\|I+T\|>1$ and $I+T$ does not attain its norm.",

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AB - It is shown that if $11$, 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 $\|I+T\|>1$ and $I+T$ does not attain its norm.

M3 - Article

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EP - 136

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

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Norm attaining operators and pseudospectrum

Abstract

ASJC Scopus subject areas

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