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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |