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On semi B-Fredholm operators. (English) Zbl 0995.47008
Summary: An operator \(T\) on a Banach space is called ‘semi B-Fredholm’ if for some \(n\in\mathbb{N}\) the range \(R(T^n)\) is closed and the induced operator \(T_n\) on \(R(T^n)\) semi-Fredholm. Semi B-Fredhom 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’.

MSC:
47A53 (Semi-) Fredholm operators; index theories
47A55 Perturbation theory of linear operators
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