Kruse, KarstenKarstenKruse2020-09-292020-09-292020-06-16Banach Journal of Mathematical Analysis 4 (14): 1509-1531 (2020-09-01)http://hdl.handle.net/11420/7406We introduce a new class FV(Ω , E) of weighted spaces of functions on a set Ω with values in a locally convex Hausdorff space E which covers many classical spaces of vector-valued functions like continuous, smooth, holomorphic or harmonic functions. Then we exploit the construction of FV(Ω , E) to derive sufficient conditions such that FV(Ω , E) can be linearised, i.e. that FV(Ω , E) is topologically isomorphic to the ε-product FV(Ω) εE where FV(Ω) : = FV(Ω , K) and K is the scalar field of E.en1735-87872020415091531BMRGhttps://creativecommons.org/licenses/by/4.0/LinearisationSemi-Montel spaceVector-valued functionsWeightε-productMathematikJournal Article10.15480/882.293010.1007/s43037-020-00072-z10.15480/882.29301712.01613Other