A unifying approach to Weyl type theorems for Banach space operators

Weyl type theorems have been proved for a considerably large number of classes of operators. In this paper, by introducing the class of quasi totally hereditarily normaloid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations f(T+K), where K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of $T+K, such that f is non constant on each of the components of its domain.