On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups

I. Akbarbaglu and S. Maghsoudi

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: Let G be a locally compact group with a fixed left Haar measure λ and Ω be a system of weights on G. In this paper, we deal with locally convex space Lp(G, Ω) equipped with the locally convex topology generated by the family of norms (∥.∥p,ω) ω∈Ω. We study various algebraic and topological properties of the locally convex space Lp(G, Ω). In particular, we characterize its dual space and show that it is a semireflexive space. Finally, we give some conditions under which Lp(G, Ω) with the convolution multiplication is a topological algebra and then characterize its closed ideals and its spectrum.

Date: 2011
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https://doi.org/10.1155/2011/947908

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:947908

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