J. Aust. Math. Soc. 77 (2004), 73–89 RELATIVELY COMPACT-LIKE PERTURBATIONS, ESSENTIAL SPECTRA AND APPLICATION

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 inL.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. 2000 Mathematics subject classification: primary 47A53, 47A55, 47G20. 1. Introduction an