Kruse, KarstenKarstenKruse2021-04-132021-04-132021-02Mathematische Nachrichten 294 (2): 354-376 (2021-02)http://hdl.handle.net/11420/8148It is a classical result that every (Formula presented.) -valued holomorphic function has a local power series representation. This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space E over (Formula presented.). Motivated by this example we try to answer the following question. Let E be a locally convex Hausdorff space over a field (Formula presented.), let (Formula presented.) be a locally convex Hausdorff space of (Formula presented.) -valued functions on a set Ω and let (Formula presented.) be an E-valued counterpart of (Formula presented.) (where the term E-valued counterpart needs clarification itself). For which spaces is it possible to lift series representations of elements of (Formula presented.) to elements of (Formula presented.) ? We derive sufficient conditions for the answer to be affirmative using Schauder decompositions which are applicable for many classical spaces of functions (Formula presented.) having an equicontinuous Schauder basis.en1522-261620212354376Wiley-VCHhttps://creativecommons.org/licenses/by/4.0/injective tensor productSchauder basisSchauder decompositionseries representationvector-valued functionMathematikJournal Article10.15480/882.317310.1002/mana.20190017210.15480/882.31731806.01889Other