Charakterizations of the Generators of Positive Semigroups on C*- and von Neumann Algebras

Generators of positive C_0-semigroups on C^*-algebras and C_0^*-semigroups on von Neumann algebras are examined. A characterization due to Bratteli and Robinson in the C_0-case is proven in the C_0^*-case. Under the additional assumptions of unitality and contractivity of the semigroup another characterization of the generator is given. This result is restated for the dual and predual semigroup.