Verlagslink DOI: 10.1002/mana.201900172
Titel: Series representations in spaces of vector-valued functions via Schauder decompositions
Sprache: Englisch
Autor/Autorin: Kruse, Karsten  
Schlagwörter: injective tensor product; Schauder basis; Schauder decomposition; series representation; vector-valued function
Erscheinungs­datum: Feb-2021
Verlag: Wiley-VCH
Quellenangabe: Mathematische Nachrichten 294 (2): 354-376 (2021-02)
Zusammenfassung (englisch): 
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
Zeitschrift: Mathematische Nachrichten 
Institut: Mathematik E-10 
Dokumenttyp: Artikel/Aufsatz
Projekt: Projekt DEAL 
Lizenz: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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