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Weyl's theorem for perturbations of paranormal operators


Authors: Pietro Aiena and Jesús R. Guillen
Journal: Proc. Amer. Math. Soc. 135 (2007), 2443-2451
MSC (2000): Primary 47A10, 47A11; Secondary 47A53, 47A55
DOI: https://doi.org/10.1090/S0002-9939-07-08582-6
Published electronically: April 10, 2007
MathSciNet review: 2302565
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Abstract: A bounded linear operator $ T\in L(X)$ on a Banach space $ X$ is said to satisfy ``Weyl's theorem'' if the complement in the spectrum of the Weyl spectrum is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this paper we show that if $ T$ is a paranormal operator on a Hilbert space, then $ T+K$ satisfies Weyl's theorem for every algebraic operator $ K$ which commutes with $ T$.


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Additional Information

Pietro Aiena
Affiliation: Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
Email: paiena@unipa.it

Jesús R. Guillen
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad UCLA, Merida, Venezuela
Email: rguillen@ula.ve

DOI: https://doi.org/10.1090/S0002-9939-07-08582-6
Keywords: Weyl's theorem, localized SVEP, paranormal operators.
Received by editor(s): June 7, 2005
Received by editor(s) in revised form: November 21, 2005
Published electronically: April 10, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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