Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies
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 defined on X, equipped with the strict topologies βz, where z=σ,∞,p,τ,t. General integral representation theorems of (βz,‖·‖F)-conti...
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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/10.1155/2015/407521 |
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| _version_ | 1832555394949447680 |
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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 defined on X, equipped with the strict topologies βz, where z=σ,∞,p,τ,t. General integral representation theorems of (βz,‖·‖F)-continuous linear operators T:Cb(X,E)→F with respect to the corresponding operator-valued measures are established. Strongly bounded and (βz,‖·‖F)-continuous operators T:Cb(X,E)→F are studied. We extend to “the completely regular setting” some classical results concerning operators on the spaces C(X,E) and Co(X,E), where X is a compact or a locally compact space. |
| format | Article |
| id | doaj-art-cc2da99878994839875b7e54bbb741f3 |
| 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-cc2da99878994839875b7e54bbb741f32025-02-03T05:48:22ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/407521407521Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict TopologiesMarian 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 defined on X, equipped with the strict topologies βz, where z=σ,∞,p,τ,t. General integral representation theorems of (βz,‖·‖F)-continuous linear operators T:Cb(X,E)→F with respect to the corresponding operator-valued measures are established. Strongly bounded and (βz,‖·‖F)-continuous operators T:Cb(X,E)→F are studied. We extend to “the completely regular setting” some classical results concerning operators on the spaces C(X,E) and Co(X,E), where X is a compact or a locally compact space.http://dx.doi.org/10.1155/2015/407521 |
| spellingShingle | Marian Nowak Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies Journal of Function Spaces |
| title | Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies |
| title_full | Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies |
| title_fullStr | Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies |
| title_full_unstemmed | Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies |
| title_short | Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies |
| title_sort | operators on spaces of bounded vector valued continuous functions with strict topologies |
| url | http://dx.doi.org/10.1155/2015/407521 |
| work_keys_str_mv | AT mariannowak operatorsonspacesofboundedvectorvaluedcontinuousfunctionswithstricttopologies |