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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1232139-3
PII: S 0002-9939(1995)1232139-3
Keywords: Locally compact groups, uniform structures, uniformly continuous functions
Article copyright: © Copyright 1995 American Mathematical Society