# Quotients of the CAR algebra

Recently, I heard about the following theorem: each nuclear separable operator space is a completely bounded quotient of the CAR algebra. Yet, I have no idea who and where proved this theorem (presuming this is true). Could anyone please indicate a reference for it?

-
Interesting question. This is very reminiscent of the fact that every nuclear separable $C^*$-algebra $A$ can be embedded into the Cuntz algebra $\mathcal{O}_2$ such that there is a conditional expectation from $\mathcal{O}_2$ onto the image of $A$. So $A$, as an operator system, is a CP quotient of $\mathcal{O}_2$. Using extension theorems for CP and CB maps, one can probably show your statement with CAR replaced by the bigger $\mathcal{O}_2$. –  Michael Jun 4 '13 at 0:03