Title of article
Approximately spectrum-preserving maps
Author/Authors
J. Alaminos، نويسنده , , J. Extremera، نويسنده , , A.R. Villena، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2011
Pages
34
From page
233
To page
266
Abstract
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 Φ :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.
© 2011 Elsevier Inc. All rights reserved.
Keywords
Kaplansky’s problem , Spectrum preservingmap , Homomorphism , Approximately multiplicative functional , Pseudospectrum , Gleason–Kahane– ? Zelazko theorem , Spectrum , Anti-homomorphism , Standard operator algebra , Approximately multiplicative map
Journal title
Journal of Functional Analysis
Serial Year
2011
Journal title
Journal of Functional Analysis
Record number
840482
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