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Relatively compact-like perturbations, essential spectra and application

Part of: Integral, integro-differential, and pseudodifferential operators General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Khalid Latrach  and
J. Martin Paoli
Khalid Latrach
Affiliation:
Départment de Mathématiques, Université de Corse, Quartier Grossetti, BP. 52, 20250 Corte, France e-mail: latrach@univ-corse.fr
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Abstract

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The purpose of this paper is to provide a detailed treatment of the behaviour of essential spectra of closed densely defined linear operators subjected to additive perturbations not necessarily belonging to any ideal of the algebra of bounded linear operators. If A denotes a closed densely defined linear operator on a Banach space X, our approach consists principally in considering the class of A-closable operators which, regarded as operators in ℒ(XA, X) (where XA denotes the domain of A equipped with the graph norm), are contained in the set of A-Fredholm perturbations (see Definition 1.2). Our results are used to describe the essential spectra of singular neutron transport equations in bounded geometries.

MSC classification

Secondary: 47A53: (Semi-) Fredholm operators; index theories 47A55: Perturbation theory 47G20: Integro-differential operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 1 , August 2004 , pp. 73 - 90
Copyright
Copyright © Australian Mathematical Society 2004

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