Operator system structures on ordered spaces

Original · EN

Given an Archimedean order unit space (V,V+,e), we construct a minimal operator system OMIN(V) and a maximal operator system OMAX(V), which are the analogues of the minimal and maximal operator spaces of a normed space. We develop some of the key properties of these operator systems and make some progress on characterizing when an operator system S is completely boundedly isomorphic to either OMIN(S) or to OMAX(S). We then apply these concepts to the study of entanglement breaking maps. We prove that for matrix algebras a linear map is completely positive from OMIN(Mₙ) to OMAX(Mₘ) if and only if it is entanglement breaking.