Choquet Order and Jordan Morphisms of Operator Algebras

Abstract

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. 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.