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arXiv · 1805.04660

Isometries between projection lattices of von Neumann algebras

Michiya Mori
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Abstract

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 I$_1$ 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. Geh\'er and P. \v{S}emrl, which is a generalization of Wigner's theorem.

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Michiya Mori. 2018-05-12. Isometries between projection lattices of von Neumann algebras. https://doi.org/10.1016/j.jfa.2018.10.011

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