Open AccessThe Local spectral theory and surjective spectrum of linear relations
Author(s) -
Maher Mnif,
A.-A. Ouled-Hmed
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i2.81
Subject(s) - surjective function , spectrum (functional analysis) , mathematics , relation (database) , characterization (materials science) , pure mathematics , banach space , core (optical fiber) , computer science , physics , quantum mechanics , telecommunications , database , optics
UDC 517.98This 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 .