Abstract
We give a complete description of order isomorphisms between operator intervals in general von Neumann algebras. For the description, we use Jordan \(^*\)-isomorphisms and locally measurable operators. Our results generalize several works by L. Molnár and P. Šemrl on type I factors.
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Acknowledgements
The author is grateful to Yasuyuki Kawahigashi, the advisor of the author, for his invaluable support, and to Gilles Pisier and the anonymous referee for helpful comments. This work was supported by Leading Graduate Course for Frontiers of Mathematical Sciences and Physics, MEXT, Japan.
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Mori, M. Order Isomorphisms of Operator Intervals in von Neumann Algebras. Integr. Equ. Oper. Theory 91, 11 (2019). https://doi.org/10.1007/s00020-019-2510-x
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DOI: https://doi.org/10.1007/s00020-019-2510-x