Operator system explained

l{A} , a

• -closed

subspace S containing 1 is called an operator system. One can associate to each subspace l{M} \subseteq l{A} of a unital C*-algebra an operator system via S: = l{M}+ l{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.^[1]

See also

• Operator space

Notes and References

1. Choi M.D., Effros, E.G. Injectivity and operator spaces. Journal of Functional Analysis 1977