Completely continuous multipliers from ${L}_{1}\left(G\right)$ into ${L}_{\infty }\left(G\right)$
Annales de l'Institut Fourier, Volume 34 (1984) no. 2, p. 137-154

For a locally compact Hausdorff group $G$ we investigate what functions in ${L}_{\infty }\left(G\right)$ give rise to completely continuous multipliers ${T}_{g}$ from ${L}_{1}\left(G\right)$ into ${L}_{\infty }\left(G\right)$. In the case of a metrizable group we obtain a complete description of such functions. In particular, for $G$ compact all $g$ in ${L}_{\infty }\left(G\right)$ induce completely continuous ${T}_{g}$.

Étant donné un groupe $G$ localement compact et séparé, nous étudions les fonctions $g$ de ${L}_{\infty }\left(G\right)$ qui induisent des convoluteurs ${T}_{g}$ complètement continus de ${L}_{1}\left(G\right)$ dans ${L}_{\infty }\left(G\right)$. Dans le cas d’un groupe métrisable nous obtenons une description complète de ces fonctions.

@article{AIF_1984__34_2_137_0,
author = {Crombez, G. and Govaerts, Willy},
title = {Completely continuous multipliers from $L\_1(G)$ into $L\_\infty (G)$},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Durand},
volume = {34},
number = {2},
year = {1984},
pages = {137-154},
doi = {10.5802/aif.968},
zbl = {0518.42009},
mrnumber = {86b:43003},
language = {en},
url = {http://www.numdam.org/item/AIF_1984__34_2_137_0}
}

Crombez, G.; Govaerts, Willy. Completely continuous multipliers from $L_1(G)$ into $L_\infty (G)$. Annales de l'Institut Fourier, Volume 34 (1984) no. 2, pp. 137-154. doi : 10.5802/aif.968. http://www.numdam.org/item/AIF_1984__34_2_137_0/

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