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Geometry of the state space of modular Jordan algebras. (English. Russian original) Zbl 0999.46500
Russ. Acad. Sci., Izv., Math. 43, No. 3, 581-592 (1994); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 6, 199-211 (1993).
Summary: In the class of compact convex sets the normal state spaces of modular Jordan algebras are characterized. To wit, the state spaces are precisely those sets that are modular, spectral and symmetric.
MSC:
46L70 Nonassociative selfadjoint operator algebras
46H70 Nonassociative topological algebras
46A55 Convex sets in topological linear spaces; Choquet theory
46K70 Nonassociative topological algebras with an involution
17C65 Jordan structures on Banach spaces and algebras
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