A note on generalized Weyl’s theorem. (English) Zbl 1101.47002

Zguitti, H.

J. Math. Anal. Appl. 316, No. 1, 373-381 (2006).

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.

Reviewer: Mohamed Zohry (Tétouan)

MSC:

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

Keywords:

single-valued extension property (SVEP); B-Fredholm operator; generalised Weyl theorem; paranormal operator

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