Given a unital C*-algebra a *-closed subspace S containing 1 is called an operator system. One can associate to each subspace of a unital C*-algebra an operator system via .
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.
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“The intellect is vagabond, and our system of education fosters restlessness. Our minds travel when our bodies are forced to stay at home. We imitate; and what is imitation but the travelling of the mind?”
—Ralph Waldo Emerson (1803–1882)