On a class of quasi-Fredholm operators. (English) Zbl 0939.47010

Summary: We study a class of bounded linear operators acting on a Banach space \(X\) called B-Fredholm operators. Among other things we characterize a B-Fredholm operator as the direct sum of a nilpotent operator and a Fredholm operator and we prove a spectral mapping theorem for B-Fredholm operators.


47A53 (Semi-) Fredholm operators; index theories
47A55 Perturbation theory of linear operators
47A10 Spectrum, resolvent
Full Text: DOI


[1] Dunford, N. and Schwartz, J.T.,Linear operators, Part 1; Wiley Inter-science, New York, 1971. · Zbl 0243.47001
[2] Grabiner, S.,Uniform ascent and descent of bounded operators; J. Math. Soc. Japan34, no. 2 (1982), 317-337. · Zbl 0477.47013
[3] Kaashoek, M.A.,Ascent, Descent, Nullity and Defect, a Note on a paper by A.E. Taylor; Math. Annalen172, (1967), 105-115. · Zbl 0152.33803
[4] Labrousse, J.P.,Les opérateurs quasi-Fredholm: une généralisation des opérateurs semi-Fredholm; Rend. Circ. Math. Palermo (2),29, (1980), 161-258. · Zbl 0474.47008
[5] Mbekhta, M. and Muller, V.,On the axiomatic theory of the spectrum, II; Studia Math.119, no. 2, (1996), 129-147. · Zbl 0857.47002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.