Kruse, KarstenKarstenKruse2023-04-052023-04-052022-12Bulletin of the Belgian Mathematical Society - Simon Stevin 29 (3): 307-331 (2022)http://hdl.handle.net/11420/15125We 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)enBulletin of the Belgian Mathematical Society - Simon Stevin20223307331Société Mathématique de Belgiqueε-productextensionFréchet-Schwartz spacesemi-Montel spacevector-valuedweightMathematikOn sequence space representation and extension of vector-valued functionsJournal Article10.36045/j.bbms.2110091808.05182Journal Article