Research article

Moroccan Journal of Pure and Applied Analysis

, 1:7

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Property (gab) through localized SVEP

  • Pietro AienaAffiliated withDEIM, Università di Palermo Viale delle Scienze Email author 
  • , Salvatore TrioloAffiliated withDEIM, Università di Palermo Viale delle Scienze


In this article we study the property (gab) for a bounded linear operator T ϵ L(X) on a Banach space X which is a stronger variant of Browder’s theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations.

Key words and phrases

Property (gab) local spectral subspaces Browder type theorems