Universal state space embeddability of Jordan-Banach algebras

Hamhalter, Jan

doi:10.1090/S0002-9939-99-04919-9

Universal state space embeddability of Jordan-Banach algebras
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Proc. Amer. Math. Soc. 127 (1999), 131-137 Request permission

Abstract:

We study extensions of states between projection structures of JB algebras and generalized orthomodular posets. It is shown that projection orthoposet of a JB algebra $A$ admits the universal extension property if and only if the Gleason theorem is valid for $A$. As a consequence we get that any positive Stone algebra–valued measure on projection lattice of a quotient of a JBW algebra without type $I_2$ direct summand extends to a positive measure on an arbitrary larger generalized orthomodular lattice.

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