The stability of property (gt) under perturbation and tensor product

Abstract

. An operator T acting on a Banach space X obeys property ( gt ) if the isolated points of the spectrum  ( T ) of T which are eigenvalues are exactly those points  of the spectrum for which T −  is an upper semi-B -Fredholm with index less than or equal to 0. In this paper we study the stability of property ( gt ) under perturbations by fi nite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T . Moreover, we study the transfer of property ( gt ) from a bounded linear operator T acting on a Banach space X and a bounded linear operator S acting on a Banach space Y to their tensor product T ⊗ S . Mathematics