Amenability of the sequence of unitary groups associated with a $C*$-algebra Ping NG 46L35$C^*$-algebrasunitary groupamenabilitynuclearityquasidiagonalityoperator spacesHaagerup tensor product We study norm topology amenability of the unitary group of a unital $C^*$-algebra, and its relations with nuclearity and stable finiteness. These considerations lead to an operator-space version of group amenability. The main result is the following: \textit{Let $\mathcal{A}$ be a unital separable simple $C^*$-algebra. 1. If $\mathcal{A}$ is nuclear and quasidiagonal, then the unitary group sequence $\{ U( \mathbb{M}_{n} (\mathcal{A})) \}_{n=1}^{\infty}$ is amenable. 2. If $\{ U(\mathbb{M}_{n} (\mathcal{A})) \}_{n=1}^{\infty}$ is amenable, then $\mathcal{A}$ is nuclear and stably finite.} Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2791 10.1512/iumj.2006.55.2791 en Indiana Univ. Math. J. 55 (2006) 1389 - 1400 state-of-the-art mathematics http://iumj.org/access/