Journal of Operator Theory

Volume 61, Issue 1, Winter 2009 pp. 133-145.

Amenability of the unitary group of the multiplier algebra of a stable AH-algebra

Authors: Dan Kucerovsky (1), and P.-W. Ng (2)
Author institution: (1) Department of Mathematics, UNB-F, Fredericton, NB E3B 5A3 Canada
(2) Mathematics Department, Univ. of Louisiana at Lafayette, 217 Maxim Doucet Hall, P.O. Box 41010, Lafayette, LA 70504-1010 USA

Summary: Let $\A$ be a unital AH-algebra, and let $G:=\U(\Mul(\A\otimes\K ))$ be the unitary group of the multiplier algebra of $\A\otimes\K$, given the strict topology. Then $G$ is amenable in the following sense: Every affine continuous action of $G$ on a compact convex set has a fixed point.

Keywords: Amenability, multiplier algebras, $C^*$-algebras, KK-theory

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