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Zbl 1101.47002
Zguitti, H.
A note on generalized Weyl's theorem. (English)
[J] J. Math. Anal. Appl. 316, No. 1, 373-381 (2006). ISSN 0022-247X

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.
[Mohamed Zohry (Tétouan)]

MSC 2000:: *47A10 Spectrum and resolvent of linear operators
47A53 (Semi-)Fredholm operators; index theories
47B20 Subnormal operators, etc.

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

Cited in: Zbl 1259.47007

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