Unbounded generalized B-Fredholm operators


  • M. Boudhief Department of Mathematics, Faculty of Sciences of Sfax BP 1171, 3000, Sfax, Tunisia




Unbounded generalized B-Fredholm operators, operator of Saphar type, generalized B-Fredholm spectrum, quasi-Fredholm operator


In this paper, we investigate a new class of unbounded linear operators, that is, the unbounded generalized B-Fredholm operators in Banach space. More explicitly, we provide a characterization of this class of operators and some of its basic properties on a Banach space. Moreover, we study the generalized B-Fredholm spectrum and we prove a perturbation result of an unbounded generalized B-Fredholm operator under a commuting power finite-rank operator.


Download data is not yet available.


P. Aiena, “Fredholm and local spectral theory, with applications to multipliers”, Kluwer Academic Publishers, Dordrecht, 2004.

M. Berkani, On a class of quasi-Fredholm operators, Integral Equations Operator Theory 34 (1999), 244 – 249.

M. Berkani, M. Boudhief, N. Moalla, Stability of essential B-spectra of unbounded linear operators and applications, Afr. Mat. 29 (2018), 1189 – 1202.

M. Berkani, N. Castro-González, Unbounded B-Fredholm operators on Hilbert spaces, Proc. Edinb. Math. Soc. (2) 51 (2) (2008), 285 – 296.

M. Berkani, N. Moalla, B-Fredholm properties of closed invertible operators, Mediterr. J. Math. 13 (2016), 4175 – 4185.

J.P. Labrousse, Les opérateurs quasi-Fredholm: une généralisation des opérateurs semi-Fredholm, Rend. Circ. Mat. Palermo (2) 29 (2) (1980), 161 – 258.

D.C. Lay, Spectral analysis using ascent, descent, nullity and defect, Math. Ann. 184 (1970), 197 – 214.

J.T. Marti, Operational calculus for two commuting closed operators, Comment. Math. Helv. 43 (1968), 87 – 97.

M. Mbekhta, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69 – 105.

M. Mbekhta, V. Muller, On the axiomatic theory of the spectrum. II, Studia Math. 119 (2) (1996), 129 – 147.

O. Garcı́a, D. Causil, J. Sanabria, C. Carpintero, New decompositions for the classes of quasi-Fredholm and semi B-Weyl operators, Linear Multilinear Algebra 68 (4) (2020), 750 – 763.

O. Garcı́a, O. Ferrer, C. Carpintero, J. Sanabria, On generalized semi B-Fredholm operators, Rend. Circ. Mat. Palermo (2) 72 (2023), 1729 – 1737.

P. Saphar, Contribution à l’étude des applications linéaires dans un espace de Banach, Bull. Soc. Math. France 92 (1964), 363 – 384.

C. Schmoeger, On operators of Saphar type, Portugal. Math. 51 (1994), 617 – 628.






Functional Analysis and Operator Theory

How to Cite

Unbounded generalized B-Fredholm operators. (2024). Extracta Mathematicae, 39(1), 37-46. https://doi.org/10.17398/2605-5686.39.1.37