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