Berkani, M. On a class of quasi-Fredholm operators. (English) Zbl 0939.47010 Integral Equations Oper. Theory 34, No. 2, 244-249 (1999). 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. Cited in 6 ReviewsCited in 80 Documents MSC: 47A53 (Semi-) Fredholm operators; index theories 47A55 Perturbation theory of linear operators 47A10 Spectrum, resolvent Keywords:B-Fredholm operators; direct sum of a nilpotent operator and a Fredholm operator; spectral mapping theorem PDF BibTeX XML Cite \textit{M. Berkani}, Integral Equations Oper. Theory 34, No. 2, 244--249 (1999; Zbl 0939.47010) Full Text: DOI References: [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.