Operator system

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