Abstract. Let H be an infinite-dimensional complex Hilbert space and let L (H ) be the algebra of all bounded linear operators on H . For ε > 0 and T ∈ L (H ) , let r ε (T ) denote the ε -pseudo spectral radius of T . We characterize surjective maps φ on L (H ) which satisfyfor all T,S ∈ L (H ) . As application, mappings from L (X) onto itself that preserve the pseudo spectrum of Jordan triple product of operators are described. We also obtain analogous results for the finite-dimensional case, without the surjectivity assumption on φ .Mathematics subject classification (2010): 47B49, 47A10, 47A25.
Let M 2 be the algebra of 2 × 2 complex matrices. For ε > 0 , complete descriptions are given of the maps of M 2 leaving invariant the ε-pseudo spectrum of A * B , where A * B stands either for the Jordan semi-triple product ABA or the skew product AB * on matrices.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.