Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions
Let Σ be a σ-algebra of subsets of a nonempty set Ω. Let be the complex vector lattice of bounded Σ-measurable complex-valued functions on Ω and let be the Banach space of all bounded countably additive complex-valued measures on Ω. We study locally solid topologies on . In particular, it is shown...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/343685 |
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| _version_ | 1832560010441261056 |
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| author | Marian Nowak |
| author_facet | Marian Nowak |
| author_sort | Marian Nowak |
| collection | DOAJ |
| description | Let Σ be a σ-algebra of subsets of a nonempty set Ω. Let be the complex vector lattice of bounded Σ-measurable complex-valued functions on Ω and let be the Banach space of all bounded countably additive complex-valued measures on Ω. We study locally solid topologies on . In particular, it is shown that the Mackey topology is the finest locally convex-solid σ-Lebesgue topology on . |
| format | Article |
| id | doaj-art-f33a682b5d1c46a29101783509f7066f |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-f33a682b5d1c46a29101783509f7066f2025-02-03T01:28:40ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/343685343685Topological Properties of the Complex Vector Lattice of Bounded Measurable FunctionsMarian Nowak0Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4A, 65-516 Zielona Góra, PolandLet Σ be a σ-algebra of subsets of a nonempty set Ω. Let be the complex vector lattice of bounded Σ-measurable complex-valued functions on Ω and let be the Banach space of all bounded countably additive complex-valued measures on Ω. We study locally solid topologies on . In particular, it is shown that the Mackey topology is the finest locally convex-solid σ-Lebesgue topology on .http://dx.doi.org/10.1155/2013/343685 |
| spellingShingle | Marian Nowak Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions Journal of Function Spaces and Applications |
| title | Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions |
| title_full | Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions |
| title_fullStr | Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions |
| title_full_unstemmed | Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions |
| title_short | Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions |
| title_sort | topological properties of the complex vector lattice of bounded measurable functions |
| url | http://dx.doi.org/10.1155/2013/343685 |
| work_keys_str_mv | AT mariannowak topologicalpropertiesofthecomplexvectorlatticeofboundedmeasurablefunctions |