Quelques observations concernant les ensembles de Ditkin d'un groupe localement compact |
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Authors: | Antoine Derighetti |
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Institution: | (1) Institut de mathématiques, Université de Lausanne, CH-1015 Lausanne-Dorigny, Suisse |
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Abstract: | We prove that every closed normal subgroupH of a locally compact amenable groupG is a Ditkin set with respect to the Herz-Figà-Talamanca algebraA
p
(G) (p>1). Let be the canonical map ofG ontoG/H andF a closed subset ofG/H. We show thatF is a Ditkin set if and only if everyuA
p
(G), which vanishes on –1, lies on the norm closure of the subspace ofA
p
(G) generated by {u
h
|hH, vA
p
(G)C
00(G)} whereu
h
(x)=u(x h). As far as we know, this result seems to be new even forG abelian andp=2. |
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Keywords: | |
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