No abstract

No 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 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).

Let B(H ) the algebra of all bounded linear operators on a complex Hilbert space H with dim H 3 . Let W , V be subsets of B(H ) which contain all rank-one operators. Denote by r ε (A) the condition spectral radius of A ∈ B(H ) . We determine the form of surjective maps (2010): Primary 47B49, Secondary 47B48, 47A10, 46H05. Mathematics subject classification

No abstract