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Spring 2018 Cover topologies, subspaces, and quotients for some spaces of vector-valued functions
Terje Hõim, D. A. Robbins
Adv. Oper. Theory 3(2): 351-364 (Spring 2018). DOI: 10.15352/AOT.1706-1177

Abstract

‎Let $X$ be a completely regular Hausdorff space‎, ‎and let $\mathcal{D}$ be a‎ ‎cover of $X$ by $C_{b}$-embedded sets‎. ‎Let $\pi‎: ‎\mathcal{E} \rightarrow X$‎ ‎be a bundle of Banach spaces (algebras)‎, ‎and let $\Gamma(\pi)$ be the‎ ‎section space of the bundle $\pi‎.‎$ Denote by $\Gamma _{b}(\pi‎,‎\mathcal{D})$‎ ‎the subspace of $\Gamma (\pi )$ consisting of sections which are bounded on‎ ‎each $D \in \mathcal{D}$. We construct a bundle $\rho ^{\prime }: \mathcal{F}‎^{\prime}\rightarrow \beta X$ such that $\Gamma _{b}(\pi‎ ,‎ \mathcal{D}) ‎$ is topologically and algebraically isomorphic to $\Gamma(\rho^\prime‎‎)‎$, ‎and use this to study the subspaces (ideals) and quotients resulting‎ ‎from endowing $\Gamma _{b}(\pi‎,‎\mathcal{D})$ with the cover topology‎ ‎determined by $\mathcal{D}$‎.

Citation

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Terje Hõim. D. A. Robbins. "Cover topologies, subspaces, and quotients for some spaces of vector-valued functions." Adv. Oper. Theory 3 (2) 351 - 364, Spring 2018. https://doi.org/10.15352/AOT.1706-1177

Information

Received: 10 June 2017; Accepted: 16 October 2017; Published: Spring 2018
First available in Project Euclid: 15 December 2017

zbMATH: 06848504
MathSciNet: MR3738216
Digital Object Identifier: 10.15352/AOT.1706-1177

Subjects:
Primary: 46H25
Secondary: 46H10

Keywords: bundle of Banach algebras , bundle of Banach spaces , cover topology

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 2 • Spring 2018
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