Disjointness preserving C0-semigroups and local operators on ordered Banach spaces

We generalize results concerning C0-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving C0-semigroup is local. Some basic properties of local operators are also given. We investigate cases where local operators generate local C0-semigroups, by using Taylor series or Yosida approximations. As norms we consider regular norms and show that bands are closed with respect to such norms. Our proofs rely on the theory of embedding pre-Riesz spaces in vector lattices and on corresponding extensions of regular norms.