Michiya Mori: Ring isomorphisms of locally measurable operator algebras

Consider a pair M, N of von Neumann algebras and their projection lattices P(M),P(N). In this talk, I will explain the following: Every lattice isomorphism from P(M) onto P(N) can be described by means of a ring isomorphism between the algebras of locally measurable operators if M has no direct summands of type I_1 and I_2. Moreover, if M has no finite type I direct summands, then every ring isomorphism between the algebras of locally measurable operators of M and N is similar to a real *-isomorphism.