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Uniform Closures of Fourier-Stieltjes Algebras

Ching Chou
Proceedings of the American Mathematical Society
Vol. 77, No. 1 (Oct., 1979), pp. 99-102
DOI: 10.2307/2042723
Stable URL: http://www.jstor.org/stable/2042723
Page Count: 4
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Uniform Closures of Fourier-Stieltjes Algebras
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Abstract

Let $H$ be a closed normal subgroup of a locally compact group $G$. Assume that $f$ is a continuous function on $G$ such that it is constant on the cosets of $H$ in $G$ and it can be approximated uniformly by coefficient functions of unitary representations of $G$. We show that $f$ can be approximated uniformly by coefficient functions of representations of $G$ which are lifted from unitary representations of $G/H$. For abelian $G$, our theorem is a conjecture of R. B. Burckel.

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