Geodesic
Weighted $L_p$-Algebras on Groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 82-85

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The space $L_p(G)$, $1$, on a locally compact group $G$ is known to be closed under convolution only if $G$ is compact. However, the weighted spaces $L_p(G,w)$ are Banach algebras with respect to convolution and natural norm under certain conditions on the weight. In the present paper, sufficient conditions for a weight defining a convolution algebra are stated in general form. These conditions are well known in some special cases. The spectrum (the maximal ideal space) of the algebra $L_p(G,w)$ on an Abelian group $G$ is described. It is shown that all algebras of this type are semisimple.
Keywords: weighted convolution algebra, Beurling algebra, multiplicative spectrum, locally compact Abelian group. 
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     author = {Yu. N. Kuznetsova},
     title = {Weighted $L_p${-Algebras} on {Groups}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {82--85},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a10/}
}
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Yu. N. Kuznetsova. Weighted $L_p$-Algebras on Groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 82-85. http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a10/