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UNBOUNDED B-FREDHOLM OPERATORS ON HILBERT SPACES

Published online by Cambridge University Press:  28 July 2008

M. Berkani  and
N. Castro-González
M. Berkani
Affiliation:
Département de Mathématiques, Faculté des Sciences, Université Mohammed I, Oujda, Morocco ([email protected])
N. Castro-González
Affiliation:
Facultad de Informática, Universidad Politécnica de Madrid, 28660 Madrid, Spain ([email protected])
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Abstract

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This paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space $H$ and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index $0$ is given in terms of the sum of a Drazin closed operator and a finite-rank operator. We analyse the properties of the powers $T^m$ of a closed B-Fredholm operator and we establish a spectral mapping theorem.

Keywords

Primary 47A5347A55unbounded B-Fredholm operatorsindexDrazin inverse
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 2 , June 2008 , pp. 285 - 296
Copyright
Copyright © Edinburgh Mathematical Society 2008