An $L^p$-version of a theorem of D.A. Raikov

Fendler, Gero

L^{p}

-version of a theorem of D.A. Raikov

Fendler, Gero

Annales de l'Institut Fourier, Tome 35 (1985), p. 125-135 / Harvested from Numdam

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Résumé
Abstract

Soit $G$ un groupe localement compact, pour $p \in (1, \infty)$ , soit $P f_{f} (G)$ l’adhérence de $L^{1} (G)$ dans les opérateurs de convolution de $L^{p} (G)$ . Désignons par $W_{p} (G)$ le dual de $P f_{p} (G)$ qui est contenu dans l’espace des multiplicateurs ponctuels de l’espace de Figà-Talamanca Herz $A_{p} (G)$ . On démontre que sur la sphère unité de $W_{p} (G)$ , la topologie $σ (W_{p}, P f_{p})$ et la topologie forte, comme multiplicateurs de $A_{p} (G)$ , coïncident.

Let $G$ be a locally compact group, for $p \in (1, \infty)$ let $P f_{p} (G)$ denote the closure of $L^{1} (G)$ in the convolution operators on $L^{p} (G)$ . Denote $W_{p} (G)$ the dual of $P f_{p} (G)$ which is contained in the space of pointwise multipliers of the Figa-Talamanca Herz space $A_{p} (G)$ . It is shown that on the unit sphere of $W_{p} (G)$ the $σ (W_{p}, P f_{p})$ topology and the strong $A_{p}$ -multiplier topology coincide.

Publié le : 1985-01-01

MR 86h:43003 | Zbl 0543.43003

DOI : https://doi.org/10.5802/aif.1002

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     author = {Fendler, Gero},
     title = {An $L^p$-version of a theorem of D.A. Raikov},
     journal = {Annales de l'Institut Fourier},
     volume = {35},
     year = {1985},
     pages = {125-135},
     doi = {10.5802/aif.1002},
     mrnumber = {86h:43003},
     zbl = {0543.43003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1985__35_1_125_0}
}

Fendler, Gero. An $L^p$-version of a theorem of D.A. Raikov. Annales de l'Institut Fourier, Tome 35 (1985) pp. 125-135. doi : 10.5802/aif.1002. http://gdmltest.u-ga.fr/item/AIF_1985__35_1_125_0/

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