Lattice isomorphisms between projection lattices of von Neumann algebras

Abstract

Generalizing von Neumann's result on type II${}_1$ von Neumann algebras, we characterize lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally measurable operators. Moreover, we give a complete description of ring isomorphisms of locally measurable operator algebras when the von Neumann algebras are without type II direct summands.

21 pages

Cited by in corpus (2)

• Ring isomorphisms of Murray--von Neumann algebras
• On regular ${}^{\ast }$-algebras of bounded linear operators: A new approach towards a theory of noncommutative Boolean algebras