operator system

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

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.Choi M.D., Effros, E.G. Injectivity and operator spaces. Journal of Functional Analysis 1977