SemiFredholm linear relations in operator rangles

The stability of semiFredholm operators under strictly singular or small perturbation in Banach spaces were studied by several authors $[9, 14, 16, 18],\dots$. The main purpose of this paper is to study this problem for semiFredholm linear relations in operator ranges. We also give properties of adjoints of semiFredholm linear relations. Examples are exhibited proving that these results are not valid in arbitrary normed spaces.