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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weyl’s theorem for perturbations of paranormal operators
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by Pietro Aiena and Jesús R. Guillen PDF
Proc. Amer. Math. Soc. 135 (2007), 2443-2451 Request permission

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
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2302565