Descent and essential descent spectrum of linear relations

Abstract

In this paper, we study the descent spectrum and the essential descent spectrum of linear relations everywhere defined on Banach spaces. We prove that the corresponding spectra are closed and we obtain that a Banach space X is finite dimensional if and only if the descent and the essential descent of every closed linear relation acting in X is finite. We give characterizations of the descent and the essential descent of linear relations and as applications, some perturbation results are presented.