Glasgow Mathematical Journal

On semi B-Fredholm operators

M.  Berkani  a1 1 and M.  Sarih  a2
a1 Université Mohammed I, Faculté des Sciences, Département de Mathématiques, Oujda, Maroc e-mail:
a2 Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, Kénitra, Maroc

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’.

(Received February 8 2000)


1 Supported by a grant of CGRI-Belgium.