Speaker: **Michiya Mori** (Univ. Tokyo)

Title: Ring isomorphisms of locally measurable operator algebras

Time/Date: 4:45-6:15pm, November 15 (Tue), 2022.

Room: 128 Math Sci Building (It will be also online. The Zoom link is the same as before. If you don't have one, please ask Kawahigashi.)

Abstract: 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.