Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.2930
Publisher DOI: 10.1007/s43037-020-00072-z
Title: Weighted spaces of vector-valued functions and the ε-product
Language: English
Authors: Kruse, Karsten  
Keywords: Linearisation;Semi-Montel space;Vector-valued functions;Weight;ε-product
Issue Date: 16-Jun-2020
Source: Banach Journal of Mathematical Analysis 4 (14): 1509-1531 (2020-09-01)
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/7406
DOI: 10.15480/882.2930
ISSN: 1735-8787
Institute: Mathematik E-10 
Document Type: Article
Project: Projekt DEAL 
More Funding information: Open Access funding provided by Projekt DEAL.
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
Journal: Banach journal of mathematical analysis 
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