Property (w) and perturbations II

This note is a continuation of a previous article [P. Aiena, M.T. Biondi, Property (w) and perturbations, J. Math. Anal. Appl. 336 (2007) 683–692] concerning the stability of property (w), a variant ofWeyl’s theorem, for a bounded operator T acting on a Banach space, under finite-dimensional perturbations K commuting with T . A counterexample shows that property (w) in general is not preserved under finite-dimensional perturbations commuting with T , also under the assumption that T is a-isoloid. © 2007 Elsevier Inc. All rights reserved.