In this paper, we introduce and study the class of k-strictly quasi-Fredholm linear relations on Banach spaces for nonnegative integer k. Then we investigate its robustness through perturbation by finite rank operators.
Alvarez, T. On regular linear relations. Acta. Math. Sini. (English Ser.) 28, 2, (2012), 183–194.
Bouaniza, H. and Mnif, M. On strictly quasi-Fredholm linear relations and semi-B-Fredholm linear relation perturbations. Filomat 31, 20 (2017), 6337–6355.
Bouaniza, H. and Mnif, M. Some Properties of Strictly Quasi-Fredholm Linear Relations. MathLAB Journal, 3 (2019), 20–38.
Chafai, E. and Mnif, M. Spectral mapping theorem for ascent, essential ascent, descent and essential descent spectrum of linear relations. Acta Math Sci. 34B, 4 (2014), 1212–1224.
Chamkha, Y. and Mnif, M. The class of B-Fredholm linear relations. Complex Anal. Oper. Theo. 9, (2015), 1681–1699.
Cross, R. On the continuous linear image of a Banach space. J. Austral. Math. Soc. (Series A) 29 (1980), 219–234.
Cross, R. An index theorem for the product of linear relations. Linear Algebra Appl. 277, (1998), 127–134.
Fakhfakh, F. and Mnif, M. Perturbation theory of lower semi-Browder multivalued linear operators. Publ. Math. Debrecen 78, 3-4 (2011), 595–606.
Garbouj, Z. and Skhiri, H. On a new class of operators related to quasi-Fredholm operators. Methods Funct. Anal. Topology 26, 2 (2020), 141–166.
Grabiner, S. Uniform ascent and descent of bounded operators. J. Math. Soc. Japan 34, 2 (1982), 317–337.
Labrousse, J.-Ph. Les opérateurs Quasi Fredholm: une généralisation des opérateurs semi-Fredholm. Rend. Circ. Mat. Palermo 29 (1980), 161–258.
Labrousse, J.-Ph., Sandovici, A., De Snoo, H. S. V., and Winkler, H. Quasi-Fredholm relations in Hilbert spaces. Studii şi Cercetări Ştiinţifice. Ser. Mat. 16 (2006), 93–106.
Muller, V. Spectral theory of linear operators and spectral systems in Banach algebras, Operator Theory: Advances and Applications Vol.139 Berlin.(2003).
Sandovici, A., De Snoo, H., and Winkler, H. Ascent, nullity, defect, and related notions for linear relations in linear spaces. Linear Algebra Appl. 423 (2007), 456–497.
Wilcox, D. Multivalued semi-Fredholm Operators in Normed Linear Spaces. Doctoral thesis, University of Cape Town, 2002.