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Operator system structures on ordered spaces

Operator system structures on ordered spaces,10.1112/plms/pdq011,Proceedings of The London Mathematical Society,VERN I. PAULSEN,IVAN G. TODOROV,Mark T

Operator system structures on ordered spaces   (Citations: 10)
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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(M_n) to OMAX(M_m) if and only if it is entanglement breaking.
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