Definition 41.2.1 (Concrete Operator System).label Let $A$ be a $C^{*}$-algebra and $S \subset A$, then $S$ is a concrete operator system if:

  1. (1)

    $1_{A} \in S$.

  2. (2)

    $S = S^{*}$.

  3. (3)

    $S$ is a linear subspace of $A$.

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