Nuclear 𝐶*-algebras have amenable unitary groups

Paterson, Alan L. T.

doi:10.1090/S0002-9939-1992-1076577-8

Nuclear $C^ *$-algebras have amenable unitary groups
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by Alan L. T. Paterson

Proc. Amer. Math. Soc. 114 (1992), 719-721

DOI: https://doi.org/10.1090/S0002-9939-1992-1076577-8

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Abstract:

Let $A$ be a unital ${C^*}$-algebra with unitary group $G$. Give $G$ the relative (Banach space) weak topology. Then $G$ is a topological group, and we show that $A$ is nuclear if and only if there exists a left invariant mean on the space of right uniformly continuous, bounded, complex-valued functions on $G$.

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