On a class of positive C_0-semigroups on weighted continuous function spaces,

This paper is mainly concerned with the study of the generators of those positive C0-semigroups on weighted continuous function spaces that leave invariant a given closed sublattice of bounded continuous functions and whose relevant restrictions are Feller semigroups. Additive and multiplicative perturbation results for this class of generators are also established. Finally, some applications concerning multiplicative perturbations of the Laplacian on Rn, n ≥ 1, and degenerate second-order differential operators on unbounded real intervals are showed.