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

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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.