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

Title: Lattice isomorphisms between projection lattices of von Neumann algebras

Time/Date: 4:45-6:15pm, April 23 (Thu.), 2020

Room: This will be an online seminar on Zoom. Details are given elsewhere.

Abstract: What is the general form of lattice isomorphisms between projection
lattices of von Neumann algebras? In 1930s, von Neumann gave an answer
to this question for type II_{1} factors. He proved that a lattice
isomorphism can be described by means of a ring isomorphism between
the algebras of affiliated operators. However, apparently no answer to
this question has been given for the general case (in particular for
type III von Neumann algebras) until now. In this talk, I give an
answer to this question for general von Neumann algebras (save type
I_{1} and I_{2}) using ring isomorphisms between the algebras of locally
measurable operators. We also consider a better description of ring
isomorphisms between locally measurable operator algebras.