Resumen de On the pseudospectrum preservers

Mustapha Ech-Cherif El Kettani, A. Lahssaini

• 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).