We prove versions of the Feller-Miyadera-Phillips theorem characterizing the generators of positive _C_0- and _C_0*-semigroups on ordered Banach spaces, for which the norm and dual norm are monotonic. Two proofs are given. The first is based on half-norm theory whilst the second exploits the existence of an equivalent Riesz norm. This latter norm exists if, and only if, the positive cone is normal and generating.
Cite this article
Derek W. Robinson, On Positive Semigroups. Publ. Res. Inst. Math. Sci. 20 (1984), no. 1, pp. 213–224DOI 10.2977/PRIMS/1195181837