Abstract
We show that ordinal isomorphisms of orthogonal measures on state spaces of operator algebras equipped with the Choquet order are generated by Jordan isomorphisms of associated von Neumann algebras. This yields a new Jordan invariant of σ-finite von Neumann algebras in terms of decompositions of states.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 140, Differential Equations. Mathematical Physics, 2017.
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Turilova, E.A., Hamhalter, J. Choquet Order and Jordan Morphisms of Operator Algebras. J Math Sci 241, 501–506 (2019). https://doi.org/10.1007/s10958-019-04439-y
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DOI: https://doi.org/10.1007/s10958-019-04439-y