Fredholm, Semi-Fredholm Perturbations, and Essential Spectra

This paper is devoted to the investigation of the stability of the various essential spectra of closed densely defined linear operators under perturbations belonging to any two-sided ideal of the algebra of bounded linear operators contained in the set of Fredholm perturbations. Our results generalize many known ones in the literature and, in particular, extend and unify those obtained by K. Latrach Ž1999, J. Math. Anal. Appl. 233, 607 623. and K. Latrach and A. Jeribi Ž1998, J. Math. Anal. Appl. 225, 461 485.. They are used to describe the essential spectra of one-dimensional transport equations with anisotropic scattering and abstract boundary conditions.