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

We generalize results concerning C-0-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving C-0-semigroup is local. Some basic properties of local operators are also given. We investigate cases where local operators generate local Co-semigroups, by using Thylor 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; (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.