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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Index of B-Fredholm operators and generalization of a Weyl theorem


Author: M. Berkani
Journal: Proc. Amer. Math. Soc. 130 (2002), 1717-1723
MSC (1991): Primary 47A53, 47A55
Published electronically: October 17, 2001
MathSciNet review: 1887019
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Abstract: The aim of this paper is to show that if $S$ and $T$ are commuting B-Fredholm operators acting on a Banach space $X$, then $ST$ is a B-Fredholm operator and $ind(ST)=ind(S)+ind(T)$, where $ind$ means the index. Moreover if $T$ is a B-Fredholm operator and $F$ is a finite rank operator, then $T+F$ is a B-Fredholm operator and $ind(T+F)= ind(T).$ We also show that if $0$ is isolated in the spectrum of $T$, then $T$ is a B-Fredholm operator of index $0$ if and only if $T$ is Drazin invertible. In the case of a normal bounded linear operator $T$ acting on a Hilbert space $H$, we obtain a generalization of a classical Weyl theorem.


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Additional Information

M. Berkani
Affiliation: Département de Mathématiques, Faculté des Sciences, Université Mohammed I, Oujda, Maroc
Email: berkani@sciences.univ-oujda.ac.ma

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06291-8
PII: S 0002-9939(01)06291-8
Received by editor(s): December 5, 2000
Published electronically: October 17, 2001
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2001 American Mathematical Society