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

TL;DR

This paper investigates the $ ol_ infty$ structure of nuclear $C^*$-algebras, establishing a threshold condition for the existence of certain representations and providing examples of quasidiagonal algebras with specific $ ol_ infty$ values.

Contribution

It proves that nuclear $C^*$-algebras with $ ol_ infty$ less than 1.005 have a family of specific representations, and constructs examples with $ ol_ infty$ greater than 1.

Findings

Nuclear $C^*$-algebras with $ ol_ infty<1.005$ have separating families of irreducible, stably finite representations.

Existence of nuclear, quasidiagonal $C^*$-algebras with $ ol_ infty>1$.

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 $\mathcal{OL}_\infty(A)>1.$