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Series representations in spaces of vector-valued functions via Schauder decompositions
Citation Link: https://doi.org/10.15480/882.3173
Publikationstyp
Journal Article
Date Issued
2021-02
Sprache
English
Author(s)
Institut
TORE-DOI
TORE-URI
Journal
Volume
294
Issue
2
Start Page
354
End Page
376
Citation
Mathematische Nachrichten 294 (2): 354-376 (2021-02)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Wiley-VCH
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.
Subjects
injective tensor product
Schauder basis
Schauder decomposition
series representation
vector-valued function
DDC Class
510: Mathematik
Publication version
publishedVersion
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