Weyl type theorems for operators satisfying the single-valued extension property

Let T be a bounded linear operator acting on a Banach space X such that T or its adjoint T ∗ has the single-valued extension property. We prove that the spectral mapping theorem holds for the B-Weyl spectrum, and we show that generalized Browder’s theorem holds for f (T ) for every analytic function f defined on an open neighborhood U of σ(T ). Moreover, we give necessary and sufficient conditions for such T to satisfy generalized Weyl’s theorem. Some applications are also given. © 2006 Elsevier Inc. All rights reserved.