On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups

I. Akbarbaglu and S. Maghsoudi

Abstract and Applied Analysis, 2011, vol. 2011, 1-15

Abstract:

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

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:947908

DOI: 10.1155/2011/947908

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