Series representations in spaces of vector-valued functions via Schauder decompositions

Karsten Kruse*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)354-376
Number of pages23
JournalMathematische Nachrichten
Volume294
Issue number2
DOIs
Publication statusPublished - Feb 2021
Externally publishedYes

Keywords

  • injective tensor product
  • Schauder basis
  • Schauder decomposition
  • series representation
  • vector-valued function

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