Quasidiagonal traces on exact C⁎-algebras

Abstract

Recently, it was proved by Tikuisis, White and Winter that any faithful trace on a separable, nuclear C⁎-algebra 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⁎-algebra in the UCT class is quasidiagonal. We also prove that any amenable trace on a separable, exact, quasidiagonal C⁎-algebra in the UCT class is quasidiagonal.