Properties of Demicompact Operators, Essential Spectra and Some Perturbation Results for Block Operator Matrices with Applications. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Jeribi, Aref; Krichen, Bilel; Zitouni, Ali
• Is Part Of: Linear & multilinear algebra. Volume 68:Issue 12(2020)
• Page Start: 2506
• Page End: 2522
• Publication Date: 2020-12-01
• Subjects: Demicompact linear operator -- essential spectrum -- Fredholm and semi-Fredholm operators -- operator matrices; 47A10 -- 47A55 -- 47A53; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1586826
• Languages: English
• ISSNs: 0308-1087

Abstract

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.