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Nonseparability and uniform structures in locally compact groups

Authors: G. Hansel and J.-P. Troallic
Journal: Proc. Amer. Math. Soc. 123 (1995), 1613-1621
MSC: Primary 22D05; Secondary 54E15
MathSciNet review: 1232139
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Abstract: Let G be a locally compact topological group. We prove that if G is not a SIN-group, then the quotient Banach space $ {\mathcal{U}_L}(G)/\mathcal{U}(G)$ contains an isometric linear copy of $ {l^\infty }$. To get this result, we first establish an extension theorem for (bilaterally) uniformly continuous functions on G.

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Keywords: Locally compact groups, uniform structures, uniformly continuous functions
Article copyright: © Copyright 1995 American Mathematical Society

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