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arXiv · 2006.08959

Lattice isomorphisms between projection lattices of von Neumann algebras

Michiya Mori
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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.

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Michiya Mori. 2020-06-16. Lattice isomorphisms between projection lattices of von Neumann algebras. https://doi.org/10.1017/fms.2020.53

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