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Weyl type theorems for operators satisfying the single-valued extension property. (English) Zbl 1117.47007
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. It is proved that the spectral mapping theorem holds for the B-Weyl spectrum. It is also shown that the generalized Browder’s theorem holds for $$f(T)$$ for every analytic function $$f$$ defined on an open neighborhood $$U$$ of $$\sigma(T)$$. Moreover, necessary and sufficient conditions for such $$T$$ to satisfy the generalized Weyl’s theorem are observed. Some applications are also given.

##### MSC:
 47A53 (Semi-) Fredholm operators; index theories 47A10 Spectrum, resolvent
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##### References:
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