JB-algebra

Summary

A JB-algebra is a real Jordan algebra with a complete norm that satisfies the same norm identities as the self-adjoint part of a C*-algebra. It is the abstract counterpart of a Jordan operator algebra. In the same way, a C*-algebra is the abstract counterpart of an algebra of operators. Every Jordan operator algebra is a JB-algebra, but the Albert algebra is a JB-algebra that is not of this form. JB-algebras were introduced by Alfsen, Shultz and Størmer.