Comparison between the different definitions of the essential spectrum and applications
Comparison between the different definitions of the essential spectrum and applications
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Date
2013-02-27
Auteurs
Benharrat Mohammed
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Université Oran1 Ahmed Ben Bella
Résumé
Our main objective in this thesis is to present the most various definitions of the essential spectrum founded in the mathematical literature, which beginning with the fundamental work of Weyl, is becoming more and more a special branch of spectral theory producing results and problems of its own. On other hand, we gives a remarkable various characteristic stability properties of the essential spectra under appropriate perturbations, as well as some equivalent descriptions of these spectra. Our contributions in this dissertation are:_ We give a survey of results concerning various essential spectra of closed linear operators in a Banach space and we give some relationships between this essential spectra and the SVEP theory.
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Mots-clés
Essential spectrum, Semi-Fredholm operators, Fredholm perturbations, Semi-regular operators, Quasi-Fredholm operators, Operators of Kato type, Generalized Kato spectrum, Closed-range spectrum, Local spectral theory, Transport operators