Properties of Demicompact Operators, Essential Spectra and Some Perturbation Results for Block Operator Matrices with Applications. Issue 12 (1st December 2020) - Jeribi, Aref; Krichen, Bilel; Zitouni, Ali
Abstract : In this paper, we use the concept of demicompactness, introduced by Petryshyn [Construction of fixed points of demicompact mappings in Hilbert space. J Math Anal Appl. 1966;14:276–284], in order to give a new characterization of the essential spectra of a 2 × 2 block operator matrix and to develop some perturbation results. Furthermore, we apply the obtained results to study some systems of differential equations and investigate the essential spectrum of two-groups of transport operators.