Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.3173
Publisher DOI: 10.1002/mana.201900172
Title: Series representations in spaces of vector-valued functions via Schauder decompositions
Language: English
Authors: Kruse, Karsten  
Keywords: injective tensor product;Schauder basis;Schauder decomposition;series representation;vector-valued function
Issue Date: Feb-2021
Publisher: Wiley-VCH
Source: Mathematische Nachrichten 294 (2): 354-376 (2021-02)
Abstract (english): 
It 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.
URI: http://hdl.handle.net/11420/8148
DOI: 10.15480/882.3173
ISSN: 1522-2616
Institute: Mathematik E-10 
Document Type: Article
Project: Projekt DEAL 
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
Journal: Mathematische Nachrichten 
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