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On sequence space representation and extension of vector-valued functions
Publikationstyp
Journal Article
Date Issued
2022-12
Sprache
English
Author(s)
Institut
Volume
29
Issue
3
Start Page
307
End Page
331
Citation
Bulletin of the Belgian Mathematical Society - Simon Stevin 29 (3): 307-331 (2022)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Société Mathématique de Belgique
Peer Reviewed
true
We give a unified approach to handle the problem of extending functions with values in a locally convex Hausdorff space E over a field K, which have weak extensions in a space F(Ω,K) of scalar-valued functions on a set Ω, to functions in a vector-valued counterpart F(Ω,E) of F(Ω,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 F(Ω,E) from a known representation of F(Ω,K)
Subjects
ε-product
extension
Fréchet-Schwartz space
semi-Montel space
vector-valued
weight
DDC Class
510: Mathematik