2-local *-automorphisms on semifinite von Neumann algebras

In the article we consider 2-local *-automorphisms of a complex and real W*- algebras. Unlike the derivation, a *-automorphism of W*-algebras does not necessarily have to be inner. Therefore, we consider approximately inner automorphisms of W*-algebras. It is proved that in a semifinite W*-algebra any 2-locally approximate inner *-automorphism is a Jordan *-automorphism. As a result, the following was obtained: 1) if M is a semifinite W*-algebra with Int(M) = Aut(M), then every 2-local *-automorphism is a Jordan *-automorphism; 2) in a semifinite factor, every 2-local approximate inner *-automorphism is a *-automorphism. Since the condition Int(M) = Aut(M) is satisfied for the injective factors of types II1 and II1, then any 2-local *-automorphism of the algebra M is a *-automorphism. Hence, in factor of type II1 any 2-local *-automorphism is a *-automorphism. At the end of the article, similar results are obtained for real W*-algebras.