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 ω be the canonical map ofG ontoG/H andF a closed subset ofG/H. We show thatF is a Ditkin set if and only if everyu∈A p (G), which vanishes on ω−1, lies on the norm closure of the subspace ofA p (G) generated by {υu h |h∈H, v∈A 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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Bibliographie
Anker, J.-Ph.: Applications de lap-induction en analyse harmonique. Comment. Math. Helv.58, 622–645 (1983).
Derighetti, A.: Relations entre les convoluteurs d'un groupe localement compact et ceux d'un sous-groupe fermé. Bull. Sc. Math.106, 69–84 (1982).
Derighetti, A.: A propos des convoluteurs d'un groupe quotient. Bull. Sc. Math.107, 3–23 (1983).
Herz, C.: Harmonic synthesis for subgroups. Ann. Inst. Fourier23/3, 91–123 (1973).
Herz, C.: Une généralisation de la notion de transformée de Fourier-Stieltjes. Ann. Inst. Fourier24/3, 145–157 (1974).
Lasser, R.: Zur Idealtheorie in Gruppenalgebren von [FIA] − B -Gruppen. Mh. Math.85, 59–79 (1978).
Lohoué, N.: Remarques sur les ensembles de synthèse des algèbres de groupe localement compact. J. Funct. Anal.13, 185–194 (1973).
Pier, J.-P.: Amenable Locally Compact Groups. New York: J. Wiley. 1984.
Reiter, H.: Classical Harmonic Analysis and Locally Compact Groups. Oxford: Clarendon Press. 1968.
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Derighetti, A. Quelques observations concernant les ensembles de Ditkin d'un groupe localement compact. Monatshefte für Mathematik 101, 95–113 (1986). https://doi.org/10.1007/BF01298924
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DOI: https://doi.org/10.1007/BF01298924