On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups
| Autor: | I. Akbarbaglu, S. Maghsoudi |
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| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Abstract and Applied Analysis, Vol 2011 (2011) |
| Druh dokumentu: | article |
| ISSN: | 1085-3375 1687-0409 |
| DOI: | 10.1155/2011/947908 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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