Journal of Operator Theory

Volume 65, Issue 2, Spring 2011 pp. 419-426.

Residually AF embeddable $C^*$-algebras

Authors: Marius Dadarlat (1) and Valentin Deaconu (2)
Author institution: (1) Department of Mathematics, Purdue University, West Lafayette IN 47907, U.S.A.
(2) Department of Mathematics and Statistics, University of Nevada, Reno NV 89557-0084, U.S.A.

Summary: Suppose that a separable exact $C^*$-algebra $A$ is KK-equivalent to a commutative $C^*$-algebra and that $A$ has a separating sequence of unital $*$-homomorphisms into simple AF-algebras. Under these conditions we show that $A$ embeds unitally in a simple AF-algebra. We apply this result to a class of amenable groups.

Keywords: $C^*$-algebra, residually AF

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