| Titre : |
Essential spectra under perturbations |
| Type de document : |
document multimédia |
| Auteurs : |
Naima Allaoui, Auteur ; Chafika Belabbaci, Directeur de thèse |
| Editeur : |
Laghouat : Université Amar Telidji - Département de mathématiques |
| Année de publication : |
2026 |
| Importance : |
78 p. |
| Accompagnement : |
1 disque optique numérique (CD-ROM) |
| Note générale : |
Option : Functional analysis and applications |
| Langues : |
Anglais (eng) |
| Résumé : |
This thesis investigates the stability of essential spectra of linear operators on Banach spaces under various classes of perturbations. After developing the foundational theory of Fredholm operators and perturbation classes — including compact, strictly singular, weakly compact, and Fredholm perturbations—we establish invariance results for the essential spectra of Gustafson, Weidmann, Kato, Wolf, Schechter, and Browder. Special attention is given to Banach spaces possessing the Dunford–Pettis property. The abstract theory is illustrated by an application to the neutron transport operator.
Keywords: Fredholm operators, essential spectrum, perturbation theory, strictly singular operators, weakly compact operators, Dunford–Pettis property, transport operator. |
| note de thèses : |
Mémoire de master en mathématiques |
Essential spectra under perturbations [document multimédia] / Naima Allaoui, Auteur ; Chafika Belabbaci, Directeur de thèse . - Laghouat : Université Amar Telidji - Département de mathématiques, 2026 . - 78 p. + 1 disque optique numérique (CD-ROM). Option : Functional analysis and applications Langues : Anglais ( eng)
| Résumé : |
This thesis investigates the stability of essential spectra of linear operators on Banach spaces under various classes of perturbations. After developing the foundational theory of Fredholm operators and perturbation classes — including compact, strictly singular, weakly compact, and Fredholm perturbations—we establish invariance results for the essential spectra of Gustafson, Weidmann, Kato, Wolf, Schechter, and Browder. Special attention is given to Banach spaces possessing the Dunford–Pettis property. The abstract theory is illustrated by an application to the neutron transport operator.
Keywords: Fredholm operators, essential spectrum, perturbation theory, strictly singular operators, weakly compact operators, Dunford–Pettis property, transport operator. |
| note de thèses : |
Mémoire de master en mathématiques |
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