Analytic core and quasi-nilpotent part of linear relations in Banach spaces

Abstract

In this paper, we investigate the notion of analytic core and quasi-nilpotent part of a linear relation. Furthermore, we are interested in studying the set of Generalized Kato linear relations to give some of their properties in connection with the analytic core and the quasi-nilpotent part. We finish by giving a perturbation result for this set of linear relations.

On isolated points of the approximate point spectrum of a closed linear relation

“…Most properties of these latter subspaces are also gathered. The stated results generalize the concepts of quasinilpotent part and the analytic core recently introduced in [12] to the setting of closed not necessary bounded linear relations. Section 3 begins by a generalization to the case of closed linear relations of [9, Theorem 3.1] stated above.…”

“…Now, let's further extend the concepts of quasinilpotent part and the analytic core developed in [11,12] to the case of closed not necessary bounded linear relations. Definition 2.1.…”