Geodesic
On semi B-Fredholm operators
Glasgow mathematical journal, Tome 43 (2001) no. 3, pp. 457-465

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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’. 
Berkani, M.; Sarih, M. On semi B-Fredholm operators. Glasgow mathematical journal, Tome 43 (2001) no. 3, pp. 457-465. doi: 10.1017/S0017089501030075
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