2020/01/01 by Michiya Mori
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Operator Algebra Research #Algorithm #Lattice (music) #Mathematics #Physics #Projection (relational algebra) #Pure mathematics #Von Neumann algebra #Von Neumann architecture #math.FA #math.OA
paper · pdf · doi:10.1017/fms.2020.53
published as Forum of Mathematics, Sigma 8 (2020) e49 · 21 pages
openalex publication_date 2020/01/01 · arxiv created 2020/06/16 · arxiv updated 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract Generalizing von Neumann’s result on type II 1 von Neumann algebras, I characterise lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally measurable operators. Moreover, I give a complete description of ring isomorphisms of locally measurable operator algebras when the von Neumann algebras are without type II direct summands.