On the gz-Kato decomposition and generalization of Koliha Drazin invertibility

In [24], Koliha proved that T ? L(X) (X is a complex Banach space) generalized Drazin invertible operator iff there exists an S commuting with such STS = and ?(T2S?T) {0} 0 < acc ?(T). Later, in [14, 34] the authors extended class of operators they also pseudo-Fredholm introduced by Mbekhta [27] other classes semi-Fredholm operators. As continuation these works, we introduce study 1zinvertible (resp., gz-Kato) which generalizes Kato-meromorphic Zivkovic-Zlatanovic Duggal [35]). Among results, prove 1z-invertible 1z-Kato ?p(T) ?q(T) ?(T2S T) (acc ?(T)). application using concept Weak SVEP at end this paper, give new characterizations Browder-type theorems.