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 . 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. ᮊ

The stability of essential spectra of a closed, densely defined linear operator A on L -spaces, 1 F p F ϱ, when A is subjected to a perturbation by a bounded p strictly singular operator was discussed in a previous paper by K. Latrach and A.Ž . Jeribi 1998, J. Math. Anal. Appl. 225, 461᎐485 . In the present paper we prove the invariance of the Gustafson᎐Weidmann, Wolf, Schechter, and Browder essential Ž . spectra of A under relatively strictly singular not necessarily bounded perturbations on these spaces. Further, a precise characterization of the Schechter essential Ž . spectrum is given. We show that these results are also valid on C ⌶ where ⌶ is a compact Hausdorff space. The results are applied to the one-dimensional transport equations with anisotropic scattering and abstract boundary conditions. ᮊ 2000 Academic Press

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The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most important classical definitions. We give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover, we establish a fine description of the Schechter essential spectrum of closed densely defined operators. These results are exploited to investigate the Schechter essential spectrum of a multidimensional neutron transport operator.