Approximately spectrum-preserving maps

被引：15

作者：

Alaminos, J. ^{[1
]}

Extremera, J. ^{[1
]}

Villena, A. R. ^{[1
]}

机构：

[1] Univ Granada, Dept Anal Matemat, Fac Ciencias, E-18071 Granada, Spain

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2011年 / 261卷 / 01期

关键词：

Spectrum; Pseudospectrum; Gleason-Kahane-Zelazko theorem; Kaplansky's problem; Spectrum preserving map; Approximately multiplicative functional; Approximately multiplicative map; Homomorphism; Anti-homomorphism; Standard operator algebra; LINEAR-MAPS; BANACH-ALGEBRAS; ADDITIVE MAPS; INVERTIBILITY; OPERATORS; MAPPINGS; MINIMUM;

D O I：

10.1016/j.jfa.2011.02.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X and Y be superreflexive complex Banach spaces and let B(X) and B(Y) be the Banach algebras of all bounded linear operators on X and Y, respectively. If a bijective linear map Phi : B(X) -> B(Y) almost preserves the spectra, then it is almost multiplicative or anti-multiplicative. Furthermore, in the case where X = Y is a separable complex Hilbert space, such a map is a small perturbation of an automorphism or an anti-automorphism. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：233 / 266

页数：34

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