Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590794 | Journal of Functional Analysis | 2011 | 11 Pages |
Abstract
We prove that an operator system S is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps φλ:S→Mnλ and ψλ:Mnλ→S such that ψλ∘φλ converges to idS in the point-norm topology. Our proof is independent of the Choi–Effros–Kirchberg characterization of nuclear C⁎-algebras and yields this characterization as a corollary. We give an explicit example of a nuclear operator system that is not completely order isomorphic to a unital C⁎-algebra.
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