Abstract
The space L p (G), 1 > p < ∞, 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.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 3, pp. 82–85, 2006
Original Russian Text Copyright © by Yu. N. Kuznetsova
The research was supported by RFBR grant no. 05-01-00982.
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Kuznetsova, Y.N. Weighted L p -algebras on groups. Funct Anal Its Appl 40, 234–236 (2006). https://doi.org/10.1007/s10688-006-0037-9
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DOI: https://doi.org/10.1007/s10688-006-0037-9