On Preserver Mappings of Spectrum and Spectral Radius of Linear Operators in Banach Spaces

Abstract

The purpose of this paper is to present some results related to the theory of pseudospectra .Given a complex Banach space X, we denote by  the algebra of all linear bounded operators on it. For , let  denote the ε-pseudospectral radius of  and denote by I the identity operator on X. For , by  we shall denote its spectrum and by  its spectral radius. For an infinite-dimensional space X, we characterize surjective maps  such that  for all . An analogous result is obtained in the finite-dimensional case, with no surjectivity assumption on the map .