On the pseudospectrum preservers





Additive maps, Pseudospectrum preservers, Generalized products


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).

Author Biographies

Mustapha Ech-Chérif El Kettani, Sidi Mohammed Ben Abdellah University.

Dept. of Mathematics, LaSMA Laboratory.

aziz lahssaini, University Sidi Mohammed Ben Abdellah.

Dept. of Mathematics, LaSMA Laboratory.


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How to Cite

M. Ech-Chérif El Kettani and aziz lahssaini, “On the pseudospectrum preservers”, Proyecciones (Antofagasta, On line), vol. 39, no. 6, pp. 1457-1469, Nov. 2020.




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