An approximation theorem for nuclear operator systems

Details An approximation theorem for nuclear operator systems An approximation theorem for nuclear operator systems

2010-09-14

arxiv.org/abs/1009.2541v4

Mathematics

Operator Algebras

10 pages; to appear in JFA

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

An approximation theorem for nuclear operator systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An approximation theorem for nuclear operator systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An approximation theorem for nuclear operator systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-394571