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 II₁ 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 I₁ and I₂) using ring isomorphisms between the algebras of locally measurable operators. We also consider a better description of ring isomorphisms between locally measurable operator algebras.