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On semi B-Fredholm operators

Published online by Cambridge University Press:  25 July 2002

M. Berkani  and
M. Sarih
M. Berkani
Affiliation:
Université Mohammed I, Faculté des Sciences, Département de Mathématiques, Oujda, Maroc e-mail: berkani@sciences.univ-oujda.ac.ma
M. Sarih
Affiliation:
Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, Kénitra, Maroc
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An operator T on a Banach space is called ‘semi B-Fredholm’ if for some n \in {\tf="times-b"N} the range R(T\;\!^n) of T\;\!^n is closed and the induced operator T_n on R(T\;\!^n) semi-Fredholm. Semi B-Fredholm operators are stable under finite rank perturbation, and subject to the spectral mapping theorem; on Hilbert spaces they decompose as sums of nilpotent and semi-Fredholm operators. In addition some recent generalizations of the punctured neighborhood theorem turn out to be consequences of Grabiner's theory of ‘topological uniform descent’.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 3 , May 2001 , pp. 457 - 465
Copyright
2001 Glasgow Mathematical Journal Trust