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

James Gabe

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arXiv · 1511.02760

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

James Gabe

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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.

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James Gabe. 2015-11-09. Quasidiagonal traces on exact $C^\ast$-algebras. https://arxiv.org/abs/1511.02760

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