Nonseparability and uniform structures in locally compact groups

Hansel, G.; Troallic, J.-P.

doi:10.1090/S0002-9939-1995-1232139-3

Nonseparability and uniform structures in locally compact groups
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by G. Hansel and J.-P. Troallic PDF

Proc. Amer. Math. Soc. 123 (1995), 1613-1621 Request permission

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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