Some remarks on the Schechter essential spectrum and applications to transport equations

The purpose of this article is to provide an extension of the work [A. Jeribi, J. Math. Anal. Appl. 271 (2002) 343–358] where a detailed treatment of the Schechter essential spectrum of a closed densely defined linear operators A subjected to additive perturbations K such that (λ−A)−1K or K(λ−A)−1 belonging to arbitrary subsets of L(X) (where X denotes a Banach spaces) contained in the ideal of Fredholm perturbations. Our approach consists principally in considering the class of A-closable (not necessarily bounded) which contained in the set of A-resolvent Fredholm perturbations (see Definition 1.12). They are used to describe the Schechter essential spectrum of singular neutron transport equations in bounded geometries.  2002 Elsevier Science (USA). All rights reserved.