TITLE: Reference request: Brown Ozawa and strong completely positive approximation property?
QUESTION [9 upvotes]: The notion of a $C^*$-algebra being nuclear has many equivalent characterisations.  These are considered in the excellent, modern textbook $C^*$-Algebras and Finite-Dimensional Approximations by Brown and Ozawa.  They take as definition that the identity on the $C^*$-algebra $A$ can be point-norm approximated by ccp maps which factor through matrix algebras.
The original definition is that there is only one $C^*$-norm on $A\odot B$, for any $B$.  In the history of the subject, Kirchberg and Choi, Effros independently showed that $A$ is nuclear if the identity on $A$ can be point-norm approximated by finite-rank ccp maps from $A$ to itself.  Kirchberg's paper calls this the strong completely positive approximation property (SCPAP) but I don't think this is common terminology now.
My questions:

Is this result in the book by Brown and Ozawa?  (Edit: By "this result" I mean precisely: that the SCPAP implies nuclearity.)  I cannot seem to find it, even though it would nicely motivate the CBAP, a weaker approximation property.
Is there any direct way to get between these two definitions?  Both papers which I cite take quite a long way around, going through work of Lance and tensor products.

My motivation is to try to give a nice, expositionary, motivation of the CBAP from nuclearity; it would be nice to point to a book for this.

REPLY [10 votes]: I am not sure if it is in Brown and Ozawa, but it is in Pisier's recent book "Tensor Products of C*-algebras and Operator Spaces" as Corollary 10.16. It may also be in his earlier Operator Spaces book, but  my copy isn't with me.