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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Nuclear $ C\sp *$-algebras have amenable unitary groups


Author: Alan L. T. Paterson
Journal: Proc. Amer. Math. Soc. 114 (1992), 719-721
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1992-1076577-8
MathSciNet review: 1076577
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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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DOI: https://doi.org/10.1090/S0002-9939-1992-1076577-8
Article copyright: © Copyright 1992 American Mathematical Society