Generators and Comparison of Entropies of Automorphisms of Finite von Neumann Algebras

We modify slightly Voiculescuʹs definition of approximation entropy of automorphisms of finite von Neumann algebras and compare it with the entropy of Connes and Stّrmer. For this the notion of a generator is relevant, as its existence implies that the entropies coincide. Special emphasis is put on binary shifts. Examples of automorphisms without generators are also considered.