On Strictly Quasi-Fredholm Linear Relations and Semi-B-Fredholm Linear Relation Perturbations

Abstract

In this paper we introduce the set of strictly quasi-Fredholm linear relations and we give some of its properties. Furthermore, we study the connection between this set and some classes of linear relations related to the notions of ascent, essentially ascent, descent ans essentially descent. The obtained results are used to study the stability of upper semi-B-Fredholm linear relations and lower semi-B-Fredholm linear relations under perturbation by finite rank operators.