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Approximately spectrum-preserving maps |
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| Authors: | J Alaminos AR Villena |
| Institution: | Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain |
| 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. |
| Keywords: | Spectrum Pseudospectrum Gleason-Kahane-?elazko theorem Kaplansky?s problem Spectrum preserving map Approximately multiplicative functional Approximately multiplicative map Homomorphism Anti-homomorphism Standard operator algebra |
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