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Titre: Comparison between the different definitions of the essential spectrum and applications

Domaine: Mathématiques informatique (MI)

Filière: Mathématique

Option: Théorie spectrale

Auteur: Benharrat Mohammed

Soutenu (e) le: 27/02/2013

Sous la direction de: Messirdi Bekkai , Professeur, Université d’Oran


Le président du jury : Bouzar Chikh, Professeur, Université d’Oran

Examinateur1: Labbas Rabah,Professeur,Université de le Havre (France)

Examinateur2: Bendoukha Berabah, Professeur, Université de Mostaganem

Examinateur3: Terbeche Mekki, Professeur, Université d’Oran

Examinateur4: Abdallah TALHAOUI, Maître de conférences–A-, ENSET d’Oran

Invité: Snoussaoui Abderrahmane, Maître de conférences –A-, Université d’Oran

Mention: Très Honorable


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.

Mots clefs: 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.

Publications associées à la thèse


Titre: Essential spectrum A Brief survey of concepts and applications

Revue: Azerbaijan Journal of Mathematics

Référence: Azerbaijan Journal of Mathematics V. 2, No 1,

Date: 2012,January

Publications associées à la thèse



Revue: Serdica Mathematical Journal

Référence: Serdica Math. J. 37 (2011), 283–294

Date: 2011