Weyl type Theorems and the Approximate Point Spectrum

Abstract

It is shown that, if an operator T on a complex Banach space or its adjoint T * has the single-valued extension property, then the generalized a-Browder's theorem holds for f (T) for every complex-valued analytic function f on a neigh-borhood of the spectrum of T . We also study the generalized a-Weyl's theorem in connection with the single-valued exten-sion property. Finally, we examine the stability of the gen-eralized a-Weyl's theorem under commutative perturbations by finite rank operators.