On $\mathcal{OL}_\infty$ structure of nuclear, quasidiagonal C*-algebras

Abstract

We continue the study of $\mathcal{OL}_\infty$ structure of nuclear $C^*$-algebras initiated by Junge, Ozawa and Ruan. In particular, we prove if $\mathcal{OL}_\infty(A)<1.005,$ then $A$ has a separating family of irreducible, stably finite representations. As an application we give examples of nuclear, quasidiagonal $C^*$-algebras $A$ with $\mathcal{OL}_\infty(A)>1.$