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.