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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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