Isometries between projection lattices of von Neumann algebras
Operator Algebras
2018-10-23 v2
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 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.
Cite
@article{arxiv.1805.04660,
title = {Isometries between projection lattices of von Neumann algebras},
author = {Michiya Mori},
journal= {arXiv preprint arXiv:1805.04660},
year = {2018}
}
Comments
16 pages, accepted for publication in J. Funct. Anal