Quantum dynamical semigroups in strongly finite von Neumann algebras (Q1848144)

Consider a von Neumann algebra \(M\) with a semigroup of normal, positive, linear and unital maps. Generalizing the analogous notions concerning groups of \(^*\)-automorphisms, the author studies finiteness, strong finiteness and several mixing properties of the semigroup. They prove the equivalence of finiteness and strong finiteness when \(M\) is atomic. Further, they prove that, when the semigroup is \({\mathbb R}_+\) and the semigroup action is strongly finite, then strongly mixing and weakly mixing are equivalent properties. Finally, they prove a characterization of exactness of the semigroup action.