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A note on generalized Weyl’s theorem. (English) Zbl 1101.47002
It is shown that, if an operator $$T$$ on a complex Hilbert space or its adjoint $$T^{*}$$ has the single-valued extension property, then the spectral mapping theorem holds for the B-Weyl spectrum. If, moreover, $$T$$ is isoloid and the generalized Weyl’s theorem holds for $$T$$, then the generalized Weyl’s theorem holds for $$f(T)$$ for every complex-valued analytic function $$f$$ on a neighborhood of the spectrum of $$T$$. Finally, an application is given for algebraically paranormal operators.

##### MSC:
 47A10 Spectrum, resolvent 47A53 (Semi-) Fredholm operators; index theories 47B20 Subnormal operators, hyponormal operators, etc.
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##### References:
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