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Abstract

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 $f\in {\mathcal H}(\sigma (T))$. 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.