Relatively strictly singular perturbations, essential spectra, and application to transport operators

[摘要] The stability of essential spectra of a closed, densely defined linear operator A on L-p-spaces, 1 less than or equal to p less than or equal to D-0, when A is subjected to a perturbation by a bounded strictly singular operator was discussed in a previous paper by K. Latrach and A. 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 spectra of A under relatively strictly singular (not necessarily bounded) perturbations on these spaces. Further, a precise characterization of the Schechter essential spectrum is given. We show that these results are also valid on C(Xi) where Xi is a compact Hausdorff space. The results are applied to the one-dimensional transport equations with anisotropic scattering and abstract boundary conditions. (C) 2000 Academic Press.

[发布日期] 2000-12-15