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Title: Spectral properties for polynomial and matrix operators involving demicompactness classes
Authors: Ben Brahim, Fatma
Jeribi, Aref
Krichen, Bilel
Keywords: Operador matricial;Operadores lineales;Operadores Fredholm y semi-Fredholm;Teoría de la perturbación;Espectros esenciales;Matrix operator;Demicompact linear operator;Fredholm and semi-Fredholm operators;Perturbation theory;Essential spectra
Issue Date: 2018
Publisher: Universidad de Extremadura
Abstract: The first aim of this paper is to show that a polynomially demicompact operator satisfying certain conditions is demicompact. Furthermore, we give a refinement of the Schmoëger and the Rakocević essential spectra of a closed linear operator involving the class of demicompact ones. The second aim of this work is devoted to provide some sufficient conditions on the inputs of a closable block operator matrix to ensure the demicompactness of its closure. An example involving the Caputo derivative of fractional of order α is provided. Moreover, a study of the essential spectra and an investigation of some perturbation results.
DOI: 10.17398/2605-5686.33.1.11
Appears in Collections:Extracta Mathematicae Vol. 33, nº 1 (2018)

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