J. Aust. Math. Soc.
77 (2004), 73-89
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Relatively compact-like perturbations, essential spectra and application
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Khalid Latrach
Département de Mathématiques
Université de Corse
Quartier Grossetti, BP. 52
20250 Corte
France
latrach@univ-corse.fr
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J. Martin Paoli
Département de Mathématiques
Université de Corse
Quartier Grossetti, BP. 52
20250 Corte
France
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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  denotes a closed densely defined linear operator
on a Banach space  , our approach consists principally in
considering the class of
 -closable operators which, regarded as operators
in  (where
 denotes the domain of
 equipped with the graph norm), are contained in
the set of  -Fredholm perturbations (see Definition 1.2).
Our results are used to describe
the essential spectra of singular neutron
transport equations in bounded geometries.
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