Operator system

Given a unital C*-algebra $𝒜$, a *-closed subspace S containing 1 is called an operator system. One can associate to each subspace $ℳ\subseteq 𝒜$ of a unital C*-algebra an operator system via $S:=ℳ+{ℳ}^{*}+ℂ1$.

The appropriate morphisms between operator systems are completely positive maps.

By a theorem of Choi and Effros, operator systems can be characterized as *-vector spaces equipped with an Archimedean matrix order.

See also

• Operator space

References

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