Jordan operator algebra

Summary

A Jordan operator algebra is a norm-closed space of self-adjoint bounded operators on a Hilbert space. It is closed under the Jordan product $\frac{1}{2}(ab + ba)$. Such algebras are also called JC-algebras, and they are concrete examples of JB-algebras. They model the observables of a quantum system. Self-adjoint operators are not closed under the ordinary product, but they are closed under the Jordan product. The theory is the Jordan analogue of the theory of C*-algebras and von Neumann algebras.