Roots for quantum ergodic theory invon Neumannʹs work

In ergodic theory von Neumann emphasized the spectral analysis of the unitary implementor and the possibility to express point translations as automorphisms over abelian algebras. Replacing the abelian algebras by noncommutative algebras good ergodic behaviour asks for type II and III algebras. The possibility for existing K-systems and Anosov systems in this framework is discussed. Von Neumnns example of a type III algebra is examined from this viewpoint.