Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology
Let X be a completely regular Hausdorff space and let E,·E and (F,·F) be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology βσ. We study the relationship between important classes of (βσ,·F)-continuous linear operators T:Cb(X...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/796753 |
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| _version_ | 1832548228661248000 |
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| author | Marian Nowak |
| author_facet | Marian Nowak |
| author_sort | Marian Nowak |
| collection | DOAJ |
| description | Let X be a completely regular Hausdorff space and let E,·E and (F,·F) be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology βσ. We study the relationship between important classes of (βσ,·F)-continuous linear operators T:Cb(X,E)→F (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. |
| format | Article |
| id | doaj-art-db5a6831619b4ea38748f237c350179e |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-db5a6831619b4ea38748f237c350179e2025-02-03T06:41:57ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/796753796753Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict TopologyMarian Nowak0Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Ulica Szafrana 4A, 65–516 Zielona Góra, PolandLet X be a completely regular Hausdorff space and let E,·E and (F,·F) be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology βσ. We study the relationship between important classes of (βσ,·F)-continuous linear operators T:Cb(X,E)→F (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived.http://dx.doi.org/10.1155/2015/796753 |
| spellingShingle | Marian Nowak Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology Journal of Function Spaces |
| title | Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology |
| title_full | Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology |
| title_fullStr | Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology |
| title_full_unstemmed | Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology |
| title_short | Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology |
| title_sort | some classes of continuous operators on spaces of bounded vector valued continuous functions with the strict topology |
| url | http://dx.doi.org/10.1155/2015/796753 |
| work_keys_str_mv | AT mariannowak someclassesofcontinuousoperatorsonspacesofboundedvectorvaluedcontinuousfunctionswiththestricttopology |