Essential spectra of some matrix operators involving γ-relatively bounded entries and an application. Issue 8 (2nd August 2016) - Jeribi, Aref; Krichen, Bilel; Zarai Dhahri, Mohammed
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.