A note on the lower Weyl and Lozanovsky spectra of a positive element

Abstract

One of the central problems investigated in Alekhno (Positivity 11(3):375–386, 2007, Positivity 13(1):3–20, 2009) is that of providing conditions under which the spectral radius of a positive operator T on a complex Banach lattice lies outside the lower Weyl spectrum of T given that it is not an element of its essential spectrum. In this paper the lower Weyl spectrum of an arbitrary positive ordered Banach algebra element is introduced and studied, and work done in the aforementioned papers are extended to general ordered Banach algebras.