Isometries between projection lattices of von Neumann algebras

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Isometries between projection lattices of von Neumann algebras

Mori, Michiya

Journal of functional analysis, 06/2019, Volume: 276, Issue: 11

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We investigate surjective isometries between projection lattices of two von Neumann algebras. We show that such a mapping is characterized by means of Jordan ⁎-isomorphisms. In particular, we prove that two von Neumann algebras without type I1 direct summands are Jordan ⁎-isomorphic if and only if their projection lattices are isometric. Our theorem extends the recent result for type I factors by G.P. Gehér and P. Šemrl, which is a generalization of Wigner's theorem.

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Mori, Michiya

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