An approximation theorem for nuclear operator systems

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We prove that an operator system S is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps ϕλ: S → Mₙλ and ψλ: Mₙλ → S such that ψλ∘ ϕλ converges to id S in the point-norm topology. Our proof is independent of the Choi-Effros-Kirchberg characterization of nuclear C*-algebras and yields this characterization as a corollary. We give an example of a nuclear operator system that is not completely order isomorphic to a unital C*-algebra.