Spectral properties for polynomial and matrix operators involving demicompactness classes
doi:10.17398/2605-5686.33.1.11
Keywords:
Matrix operator, Demicompact linear operator, Fredholm and semi-Fredholm operators, Perturbation theory, Essential spectraAbstract
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.
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