Discrete amenable group actions on von Neumann algebras and invariant nuclear C*-subalgebras

摘要: Let $G$ be a countable discrete amenable group, ${\cal M}$ McDuff factor von Neumann algebra, and $A$ separable nuclear weakly dense C$^*$-subalgebra of M}$. We show that if two centrally free actions on differ up to approximately inner automorphisms then they are outer conjugate by an automorphism, in the operator norm topology, which makes invariant. In addition, when is unital, simple, with unique tracial state $\alpha$ automorphism we also aperiodicity algebra equivalent weak Rohlin property.