On the pseudospectrum preservers
Abstract Let X and Y be two complex Banach spaces, and let B(X) denotes the algebra of all bounded linear operators on X. We characterize additive maps from B(X) onto B(Y ) compressing the pseudospectrum subsets Δ ϵ (.), where Δ ϵ (.) stands for any one of the...
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| Auteurs principaux: | , |
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| Langue: | English |
| Publié: |
Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Accès en ligne: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000601457 |
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| Résumé: | Abstract Let X and Y be two complex Banach spaces, and let B(X) denotes the algebra of all bounded linear operators on X. We characterize additive maps from B(X) onto B(Y ) compressing the pseudospectrum subsets Δ ϵ (.), where Δ ϵ (.) stands for any one of the spectral functions σ ϵ (.), σ l ϵ (.) and σ r ϵ (.) for some ϵ > 0. We also characterize the additive (resp. non-linear) maps from B(X) onto B(Y) preserving the pseudospectrum σ ϵ (.) of generalized products of operators for some ϵ > 0 (resp. for every ϵ > 0). |
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