Operator system

Given a unital C*-algebra A , a *-closed subspace S containing 1 is called an operator system. One can associate to each subspace M ⊆ A of a unital C*-algebra an operator system via S := M + M ∗ + 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.