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arXiv · 2206.00875

Ring isomorphisms of type II$_\infty$ locally measurable operator algebras

Michiya Mori
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Abstract

We show that every ring isomorphism between the algebras of locally measurable operators for type II$_\infty$ 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.

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Michiya Mori. 2022-06-02. Ring isomorphisms of type II$_\infty$ locally measurable operator algebras. https://arxiv.org/abs/2206.00875

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