Koecher–Vinberg theorem

In operator algebra, the Koecher–Vinberg theorem is a reconstruction theorem for real Jordan algebras. It was proved independently by Max Koecher in 1957 and Ernest Vinberg in 1961. It provides a one-to-one correspondence between formally real Jordan algebras and so-called domains of positivity. Thus it links operator algebraic and convex order theoretic views on state spaces of physical systems.

A convex cone ${\displaystyle C}$ is called regular if ${\displaystyle a=0}$ whenever both ${\displaystyle a}$ and ${\displaystyle -a}$ are in the closure ${\displaystyle {\overline {C}}}$.

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