On essentially semi regular linear relations

The characterization of bounded essentially semi regular operators in terms of Kato decomposition of finite type was studied by several authors. In this paper, we extend this characterization to the case of essentially semi regular linear relations. We also give other characterization of such linear relations. Further, we apply the obtained results to analyse the stability of the class of essentially semi regular linear relations under additional operator perturbations. Finally, as an application, we get some useful connections between the Fredholm spectrum and the essentially semi regular spectrum of linear relations.