Abstract
Let X be a completely regular Hausdorff space, and let C b (X) denote the Banach space of all real-valued bounded continuous functions on X. We study linear operators from C b (X) provided with the strict topology β σ to a Banach space \({(E,\|\cdot\|_E)}\). In particular, we derive a Yosida–Hewitt type decomposition for weakly compact operators from C b (X) to E.
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The author is grateful to the referee for the valuable remarks.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nowak, M. Linear operators on the space of bounded continuous functions with strict topologies. Positivity 14, 831–839 (2010). https://doi.org/10.1007/s11117-010-0068-6
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DOI: https://doi.org/10.1007/s11117-010-0068-6
Keywords
- Space of bounded continuous functions
- Strict topologies
- Baire measures
- σ-Dini topologies
- Weakly compact operators
- Yosida–Hewitt decomposition
- Generalized DF-space