On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups
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...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/947908 |
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| author | I. Akbarbaglu S. Maghsoudi |
| author_facet | I. Akbarbaglu S. Maghsoudi |
| author_sort | I. Akbarbaglu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-400d7dfa684d4ed48fb8f779276f5ce3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-400d7dfa684d4ed48fb8f779276f5ce32025-02-03T06:01:42ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/947908947908On the Generalized Weighted Lebesgue Spaces of Locally Compact GroupsI. Akbarbaglu0S. Maghsoudi1Department of Mathematics, Zanjan University, Zanjan 45195-313, IranDepartment of Mathematics, Zanjan University, Zanjan 45195-313, IranLet 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.http://dx.doi.org/10.1155/2011/947908 |
| spellingShingle | I. Akbarbaglu S. Maghsoudi On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups Abstract and Applied Analysis |
| title | On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups |
| title_full | On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups |
| title_fullStr | On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups |
| title_full_unstemmed | On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups |
| title_short | On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups |
| title_sort | on the generalized weighted lebesgue spaces of locally compact groups |
| url | http://dx.doi.org/10.1155/2011/947908 |
| work_keys_str_mv | AT iakbarbaglu onthegeneralizedweightedlebesguespacesoflocallycompactgroups AT smaghsoudi onthegeneralizedweightedlebesguespacesoflocallycompactgroups |