We introduce the families of left and right B-Fredholm operators in a Banach space, realize their stabilization with the help of finite-rank operators, and prove a spectral mapping theorem for the left and right B-Fredholm operators.
Similar content being viewed by others
References
M. Berkani, “On a class of quasi-Fredholm operators,” Integral Equations Operator Theory, 34, 244–249 (1999).
M. Berkani and M. Sarih, “On semi B-Fredholm operators,” Glasgow Math. J., 43, 457–465 (2001).
A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, 2nd edn., Inverse and Ill-Posed Problems, Ser., 59, De Gruyter, Berlin (2016).
M. A. Kaashoek, “Ascent, descent, nullity and defect, a note on a paper by A. E. Taylor,” Math. Ann., 172, 105–115 (1967).
J. P. Labrousse, “Les Opérateurs quasi-Fredholm: Une généralisation des opérateurs semi-Fredholm,” Rend. Circ. Mat. Palermo (2), 29, 161–258 (1980).
V. Kordula and V. Muller, “On the axiomatic theory of the spectrum,” Stud. Math., 119, No. 2, 109–128 (1996).
M. Mbekhta and V. Muller, “On the axiomatic theory of the spectrum, II,” Stud. Math., 119, No. 2, 129–147 (1996).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 10, pp. 1299–1307, October, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i10.6331.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Abdmouleh, F., Lakhal, T.B. Left and Right B-Fredholm Operators. Ukr Math J 74, 1479–1489 (2023). https://doi.org/10.1007/s11253-023-02149-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-023-02149-y