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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FAA_2006_40_3_a10,
     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/}
}
TY  - JOUR
AU  - Yu. N. Kuznetsova
TI  - Weighted $L_p$-Algebras on Groups
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2006
SP  - 82
EP  - 85
VL  - 40
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a10/
LA  - ru
ID  - FAA_2006_40_3_a10
ER  - 
%0 Journal Article
%A Yu. N. Kuznetsova
%T Weighted $L_p$-Algebras on Groups
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2006
%P 82-85
%V 40
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a10/
%G ru
%F FAA_2006_40_3_a10
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/

[1] S. Saeki, Illinois J. Math., 34:3 (1990), 614–627 | DOI | MR | Zbl

[2] N. K. Nikolskii, Trudy MIAN, 120, 1974 | Zbl

[3] S. Grabiner, Amer. J. Math., 97:1 (1975), 16–42 | DOI | MR | Zbl

[4] R. Kerman, E. Sawyer, Stud. Math., 108:2 (1994), 103–126 | DOI | MR | Zbl

[5] A. Benazzouz, A. El Kinani, Bull. Belg. Math. Soc. Simon Stevin, 10:1 (2003), 49–57 | DOI | MR | Zbl

[6] S. A. Shkarin, Yu. N. Kuznetsova, J. Math. Sci. (New York), 131:6 (2005), 6112–6119 | DOI | MR

[7] H. G. Dales, Radical Banach algebras and automatic continuity (Proc. Conf., Long Beach 1981), Lecture Notes in Math., 975, 1983 | MR | Zbl

[8] E. Khyuitt, K. Ross, Abstraktnyi garmonicheskii analiz, t. I, II, Nauka, M., 1975 | MR