Quasidiagonal traces on exact $C^{\ast }$-algebras

Abstract

Recently, it was proved by Tikuisis, White and Winter that any faithful trace on a separable, nuclear $C^{\ast }$-algebras in the UCT class is quasidiagonal. Building on their work, we generalise the result, and show that any faithful, amenable trace on a separable, exact $C^{\ast }$-algebras in the UCT class is quasidiagonal. We also prove that any amenable trace on a separable, exact, quasidiagonal $C^{\ast }$-algebra in the UCT class is quasidiagonal.

13 pages

References in corpus (3)

• Completely positive maps of order zero
• Classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras
• Absorbing representations with respect to closed operator convex cones

Cited by in corpus (1)

• Decomposable approximations revisited