Essential spectra of some matrix operators involving γ-relatively bounded entries and an application. Issue 8 (2nd August 2016)

• Record Type: Journal Article
• Authors: Jeribi, Aref; Krichen, Bilel; Zarai Dhahri, Mohammed
• Is Part Of: Linear & multilinear algebra. Volume 64:Issue 8(2016)
• Page Start: 1654
• Page End: 1668
• Publication Date: 2016-08-02
• Subjects: Fredholm theory -- relatively bounded operator -- measure of noncompactness -- essential spectrum; 39B42 -- 47A55 -- 47A53 -- 47A10; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2015.1112344
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : In this paper, we introduce the concept of relative boundedness with respect to an axiomatic measure of noncompactness, as a generalization of the notion of relative boundedness. Then, some spectral properties of a unbounded block operator matrix involving -relatively bounded inputs are given. The obtained results are applied to investigate the essential spectra of a two-dimensional transport operator in with abstract boundary conditions relating the incoming and the outgoing fluxes.