Given a
unital C*-algebra
In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continuou ...
, 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 map
In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one which satisfies a stronger, more robust condition.
Definition
Let A and B be C*-algebras. A linear ...
s.
By a theorem of Choi and Effros, operator systems can be characterized as *-vector spaces equipped with an Archimedean matrix order.
[Choi M.D., Effros, E.G. Injectivity and operator spaces. Journal of Functional Analysis 1977]
See also
*
Operator space
References
Operator theory
Operator algebras
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