Additive mappings preserving minimum and surjectivity moduli

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.

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Approximately spectrum-preserving maps

Alaminos

Extremera

Villena

2011

Journal of Functional Analysis

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Nonlinear maps preserving the minimum and surjectivity moduli

Bourhim¹,

Mashreghi²,

Anush³

2014

Linear Algebra and its Applications

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Spectral preservers and approximate spectral preservers on operator algebras

Alaminos

Extremera

Villena

2016

Linear Algebra and its Applications

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Additive mappings preserving minimum and surjectivity moduli

Cited by 4 publications

References 17 publications

Approximately spectrum-preserving maps

Approximately spectrum-preserving maps

Nonlinear maps preserving the minimum and surjectivity moduli

Spectral preservers and approximate spectral preservers on operator algebras

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