Ring isomorphisms of type II_∞ locally measurable operator algebras

2022/06/02 by Michiya Mori, Mori, Michiya
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2206.00875

Abstract

We show that every ring isomorphism between the algebras of locally measurable operators for type II_∞ von Neumann algebras is similar to a real ^*-isomorphism. This together with previous results by the author and Ayupov--Kudaybergenov completely describes ring isomorphisms between the algebras of locally measurable operators as well as lattice isomorphisms between the projection lattices for a general pair of von Neumann algebras without finite type I direct summands.

Related

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• 2-Local derivations on algebras of locally measurable operators
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• Local And 2-Local Derivations On Algebras Of Measurable Operators