On the pseudospectrum preservers

• Ech-Chérif El Kettani, Mustapha ^[1] ; lahssaini, aziz ^[2]
  1. [1] Sidi Mohammed Ben Abdellah University.
  2. [2] University Sidi Mohammed Ben Abdellah.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 6, 2020, págs. 1457-1469
• Idioma: inglés
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• Resumen

  • 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 ??(.), where ?? (.) stands for any one of the spectral functions ?? (.), ?l? (.) and ?r?  (.) for some ? > 0. We also characterize the additive (resp. non-linear) maps from B(X) onto B(Y) preserving the pseudospectrum ?? (.) of generalized products of operators for some ? > 0 (resp. for every ? > 0).