An L p -version of a theorem of D.A. Raikov
Annales de l'Institut Fourier, Volume 35 (1985) no. 1, p. 125-135
Let G be a locally compact group, for p(1,) let Pf p (G) denote the closure of L 1 (G) in the convolution operators on L p (G). Denote W p (G) the dual of Pf 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 ,Pf p ) topology and the strong A p -multiplier topology coincide.
Soit G un groupe localement compact, pour p(1,), soit Pf 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 Pf 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 ,Pf p ) et la topologie forte, comme multiplicateurs de A p (G), coïncident.
@article{AIF_1985__35_1_125_0,
     author = {Fendler, Gero},
     title = {An $L^p$-version of a theorem of D.A. Raikov},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {35},
     number = {1},
     year = {1985},
     pages = {125-135},
     doi = {10.5802/aif.1002},
     zbl = {0543.43003},
     mrnumber = {86h:43003},
     language = {en},
     url = {http://www.numdam.org/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, Volume 35 (1985) no. 1, pp. 125-135. doi : 10.5802/aif.1002. http://www.numdam.org/item/AIF_1985__35_1_125_0/

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