The Local spectral theory and surjective spectrum of linear relations

Abstract

UDC 517.98 This paper initiates a study of local spectral theory for linear relations. At the beginning, we define the local spectrum and study its properties. Then we obtain results related to the correlation analytic core and quasinilpotent part of a linear relation in a Banach space . As an application, we give a characterization of the surjective spectrum in terms of the local spectrum and show that if , then does not cluster at .