A characterization of the Schechter essential spectrum on Banach spaces and applications

In a recent article by the author (C. R. Acad. Sci. Paris Sér. I 331 (2000) 525–530; Boll. Un. Mat. Ital. (2002), to appear) the Schechter spectrum of closed, densely defined linear operators has been characterized on spaces, which possess the Dunford–Pettis property or which are isomorphic to one of the spaces Lp(Ω),p >1. The purpose of the present work is to extend this analysis to the case of Banach spaces. Further we apply the obtained results to investigate the Schechter essential spectrum of one-dimensional transport equations with different boundary conditions.  2002 Elsevier Science (USA). All rights reserved.