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An Approximation Theorem for Nuclear Operator Systems by Han, Kyung Hoon; Paulsen, Vern I. is a scholarly article available to read on EtoBox.

What is An Approximation Theorem for Nuclear Operator Systems about?

We prove that an operator system $\mathcal S$ is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps $\phi_\lambda : \cl S \to M_{n_\lambda}$ and $\psi_\lambda : M_{n_\lambda} \to \cl S$ such that $\psi_\lambda \circ \phi_\lambda$ converges to ${\rm id}_{\cl S}$ 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 example of a nuclear operator system that is not completely order isomorphic to a unital $C^*$-algebra.

Author

Han, Kyung Hoon; Paulsen, Vern I.

Published

2010

Language

EN