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Weighted spaces of vector-valued functions and the ε-product
Citation Link: https://doi.org/10.15480/882.2930
Publikationstyp
Journal Article
Publikationsdatum
2020-06-16
Sprache
English
Author
Kruse, Karsten
Institut
TORE-URI
Enthalten in
Volume
14
Issue
4
Start Page
1509
End Page
1531
Citation
Banach Journal of Mathematical Analysis 4 (14): 1509-1531 (2020-09-01)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
BMRG
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.
Schlagworte
Linearisation
Semi-Montel space
Vector-valued functions
Weight
ε-product
DDC Class
510: Mathematik