A note on generalized Weyl's theorem (Q819717)

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.