Quasi-Compact Perturbations of the Weyl Essential Spectrum and Application to Singular Transport Operators

Abstract

This paper is devoted to the investigation of the stability of the Weyl essential spectrum of closed densely dened linear operator A subjected to additive perturbation K such that (lambda-AK)^{-1} K or K (lambda-AK)^{-1} is a quasi-compact operator. The obtained results are used to describe the Weyl essential spectrum of singular neutron transport operator.