Geodesic
On the Radon-Nikodym property in Jordan algebras
Glasgow mathematical journal, Tome 24 (1983) no. 2, pp. 185-189

Voir la notice de l'article provenant de la source Cambridge University Press

Banach spaces whose duals possess the Radon-Nikodym property have been studied extensively in the past (cf. [5]). It has been shown recently in [4] that a C*-algebra is scattered if and only if its Banach dual possesses the Radon-Nikodym property. This result extends the well-known result of Pełczynski and Semandini [8] that a compact Hausdorff space Ωis dispersed if and only if C(Ω)* has the Radon-Nikodym property. The purpose of this note is to give a transparent proof of a more general result for Jordan algebras which unifies the aforementioned results. We prove that the dual of a JB-algebra A possesses the Radon-Nikodym property if and only if the state space of A is the cr-convex hull of its pure states. We also consider the projective tensor products of the duals of JB-algebras in this context. 
Chu, Cho-Ho. On the Radon-Nikodym property in Jordan algebras. Glasgow mathematical journal, Tome 24 (1983) no. 2, pp. 185-189. doi: 10.1017/S0017089500005279
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