A Characterization of Some Subsets of Essential Spectra of a Multivalued Linear Operator

Abstract

In the present paper, we characterize some essential spectra of a closed linear relation in terms of certain linear relations type $$\mathbf{ \alpha }$$ -and $$\beta $$ -Atkinson. This study leads us to generalize some well-known results for operators and to extend some results of small perturbations given by Alvarez and Wilcox in [6]. In the same way, we present the perturbation classes of $$\alpha $$ - and $$\beta $$ - Atkinson linear relations (see Theorem 3.3).