Spectral properties for polynomial and matrix operators involving demicompactness classes

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Spectral properties for polynomial and matrix operators involving demicompactness classes

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Title: Spectral properties for polynomial and matrix operators involving demicompactness classes
Author: Ben Brahim, Fatma; Jeribi, Aref; Krichen, Bilel
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.
URI: http://hdl.handle.net/10662/8344
Date: 2018


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