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A characterization of discrete groups

Author: Giovanni Ranieri
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1845-1848
MSC (2000): Primary 22D15
Published electronically: December 23, 2003
MathSciNet review: 2051149
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Abstract: The purpose of this article is to prove the following result. Let $G$ be a locally compact group, $\mathcal{A}(G)$ the Fourier algebra of $G,$ and $\mathcal{S} (G)=\{ u\in\mathcal{A}(G) :~\exists~c>~0$ such that $ \parallel uv\parallel_{\mathcal{A}(G)}\leq~c\parallel v\parallel_{\infty}\hspace{0.2 cm}\forall ~ v\in \mathcal{A}(G)\}$. Then $G$ is a discrete group $\Longleftrightarrow \mathcal{S} (G)~\neq \{0\}$.

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Additional Information

Giovanni Ranieri
Affiliation: Institut de Recherche Mathématique Avancée, 7 rue René Descartes, 67000 Strasbourg, France

Received by editor(s): October 9, 2002
Received by editor(s) in revised form: February 11, 2003
Published electronically: December 23, 2003
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society

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