Weighted spaces of vector-valued functions and the ε -product

Karsten Kruse*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)
2 Downloads (Pure)

Abstract

We introduce a new class FV(Ω , E) of weighted spaces of functions on a set Ω with values in a locally convex Hausdorff space E which covers many classical spaces of vector-valued functions like continuous, smooth, holomorphic or harmonic functions. Then we exploit the construction of FV(Ω , E) to derive sufficient conditions such that FV(Ω , E) can be linearised, i.e. that FV(Ω , E) is topologically isomorphic to the ε-product FV(Ω) εE where FV(Ω) : = FV(Ω , K) and K is the scalar field of E.

Original languageEnglish
Pages (from-to)1509-1531
Number of pages23
JournalBanach Journal of Mathematical Analysis
Volume14
Issue number4
DOIs
Publication statusPublished - 1 Sept 2020
Externally publishedYes

Keywords

  • Linearisation
  • Semi-Montel space
  • Vector-valued functions
  • Weight
  • ε-product

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