Weyl's and Browder's theorems for operators satisfying the SVEP

We study Weyl's and Browder's theorem for an operator T on a Banach space such that T or its adjoint has the single-valued extension property. We establish the spectral mapping theorem for the Weyl spectrum, and we show that Browder's theorem holds for f (T) for every f is an element of H(sigma(T)). Also, we give necessary and sufficient conditions for such T to obey Weyl's theorem. Weyl's theorem in an important class of Banach space operators is also studied.