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Weyl's theorem for perturbations of paranormal operators
Author(s):
Pietro
Aiena;
Jesús
R.
Guillen
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2443-2451.
MSC (2000):
Primary 47A10, 47A11;
Secondary 47A53, 47A55
Posted:
April 10, 2007
MathSciNet review:
2302565
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Abstract:
A bounded linear operator  on a Banach space  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  is a paranormal operator on a Hilbert space, then  satisfies Weyl's theorem for every algebraic operator  which commutes with  .
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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:
10.1090/S0002-9939-07-08582-6
PII:
S 0002-9939(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
Posted:
April 10, 2007
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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