Kruse, KarstenKarstenKruse2021-12-102021-12-102022-01Annals of Functional Analysis 13 (1): 1-26 (2022-02)http://hdl.handle.net/11420/11248In this paper we study the problem of extending functions with values in a locally convex Hausdorff space E over a field K, which has weak extensions in a weighted Banach space Fν(Ω,K) of scalar-valued functions on a set Ω, to functions in a vector-valued counterpart Fν(Ω,E) of Fν(Ω,K). Our findings rely on a description of vector-valued functions as continuous linear operators and extend results of Frerick, Jordá and Wengenroth. As an application we derive weak-strong principles for continuously partially differentiable functions of finite order and vector-valued versions of Blaschke’s convergence theorem for several spaces.en2008-875220221126Springer International Publishinghttps://creativecommons.org/licenses/by/4.0/extensionvector-valuedepsilon-productweightweak-strong principleMathematikJournal Article10.15480/882.401710.1007/s43034-021-00154-510.15480/882.40171910.01952Journal Article