Preservers of pseudo spectra of operator Jordan triple products

Abstract

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.