Geodesic
Lattice isomorphisms between projection lattices of von Neumann algebras
Forum of Mathematics, Sigma, Tome 8 (2020)

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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. 
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     author = {Michiya Mori},
     title = {Lattice isomorphisms between projection lattices of von {Neumann} algebras},
     journal = {Forum of Mathematics, Sigma},
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     year = {2020},
     doi = {10.1017/fms.2020.53},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.53/}
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Michiya Mori. Lattice isomorphisms between projection lattices of von Neumann algebras. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.53

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