Some results of Fredholm perturbations of multivalued linear operator in normed spaces

Aymen Ammar, Aicha Ben Ezzadam, Aref Jeribi

In the present paper, we establish first the relation between the perturbation of upper Fredholm and strictly singular, and then the relation between lower semi-Fredholm and strictly cosingular linear relations. Most importantly in Theorem 3.4, we show that P(F − (X, Y)) coincides with SC(X, Y). We bring to light, the relationship between the essential spectra of a multivalued linear operator and its selection.