Property (gw) and perturbations (Q657676)

This paper investigates the preservation of property (gw), which is a variant of the generalized Weyl's theorem, for a bounded operator \(T\) acting on a Banach space. This preservation is studied under finite rank perturbations commuting with the operator \(T\), whenever \(T\) is isoloid, polaroid, or \(T\) has analytical core \(K({\lambda}_{0}I-T)=\{0\}\) for some complex \({\lambda}_{0}\). It is also studied under commuting nilpotent or under algebraic perturbations.