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Homogeneous self dual cones versus Jordan algebras. The theory revisited

Jean BellissardB. Iochum — 1978

Annales de l'institut Fourier

Let 𝔐 be a Jordan-Banach algebra with identity 1, whose norm satisfies: (i) a b a b ,    a , b 𝔐 (ii) a 2 = a 2 (iii) a 2 a 2 + b 2 . 𝔐 is called a JB algebra (E.M. Alfsen, F.W. Shultz and E. Stormer, Oslo preprint (1976)). The set 𝔐 + of squares in 𝔐 is a closed convex cone. ( 𝔐 , 𝔐 + , 1 ) is a complete ordered vector space with 1 as a order unit. In addition, we assume 𝔐 to be monotone complete (i.e. 𝔐 coincides with the bidual 𝔐 * * ),...

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