Operator system

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 $S:={\mathcal {M}}+{\mathcal {M}}^{*}+\mathbb {C} 1$.