Operator system structures on ordered spaces
Operator Algebras
2014-02-26 v2
Abstract
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.
Cite
@article{arxiv.0904.3783,
title = {Operator system structures on ordered spaces},
author = {Vern Paulsen and Ivan Todorov and Mark Tomforde},
journal= {arXiv preprint arXiv:0904.3783},
year = {2014}
}
Comments
30 pages; Version II Comments: A couple references added, some small changes made in Section 6