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.
Famous quotes containing the word system:
“For the universe has three children, born at one time, which reappear, under different names, in every system of thought, whether they be called cause, operation, and effect; or, more poetically, Jove, Pluto, Neptune; or, theologically, the Father, the Spirit, and the Son; but which we will call here, the Knower, the Doer, and the Sayer. These stand respectively for the love of truth, for the love of good, and for the love of beauty.”
—Ralph Waldo Emerson (1803–1882)