Open AccessOn the pseudospectrum preservers
Author(s) -
Mustapha Ech-Chérif El Kettani,
A. Lahssaini
Publication year - 2020
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.226
H-Index - 12
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-2020-06-0089
Subject(s) - linear operators , bounded function , banach space , mathematics , linear map , linear algebra , spectral properties , combinatorics , algebra over a field , pure mathematics , discrete mathematics , mathematical analysis , physics , geometry , astrophysics
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 Δϵ(.), where Δϵ (.) stands for any one of the spectral functions σϵ (.), σlϵ (.) and σrϵ (.) for some ϵ > 0. We also characterize the additive (resp. non-linear) maps from B(X) onto B(Y) preserving the pseudospectrum σϵ (.) of generalized products of operators for some ϵ > 0 (resp. for every ϵ > 0).