december 2022 On sequence space representation and extension of vector-valued functions
Karsten Kruse
Bull. Belg. Math. Soc. Simon Stevin 29(3): 307-331 (december 2022). DOI: 10.36045/j.bbms.211009

Abstract

We give a unified approach to handle the problem of extending functions with values in a locally convex Hausdorff space $E$ over a field $\mathbb{K}$, which have weak extensions in a space $\mathcal{F}(\Omega,\mathbb{K})$ of scalar-valued functions on a set $\Omega$, to functions in a vector-valued counterpart $\mathcal{F}(\Omega,E)$ of $\mathcal{F}(\Omega,\mathbb{K})$. The results obtained are based upon a representation of vector-valued functions as linear continuous operators and extend results of Bonet, Frerick, Gramsch and Jordá. In particular, we apply them to obtain a sequence space representation of $\mathcal{F}(\Omega,E)$ from a known representation of $\mathcal{F}(\Omega,\mathbb{K})$.

Citation

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Karsten Kruse. "On sequence space representation and extension of vector-valued functions." Bull. Belg. Math. Soc. Simon Stevin 29 (3) 307 - 331, december 2022. https://doi.org/10.36045/j.bbms.211009

Information

Published: december 2022
First available in Project Euclid: 22 March 2023

Digital Object Identifier: 10.36045/j.bbms.211009

Subjects:
Primary: 46E40
Secondary: 46A03 , 46E10

Keywords: $\varepsilon$-product , Extension‎ , Fréchet-Scwarz space , semi-Montel space , vector-valued , weight

Rights: Copyright © 2022 The Belgian Mathematical Society

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Vol.29 • No. 3 • december 2022
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