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The approximation property for weighted spaces of differentiable functions
Publikationstyp
Journal Article
Date Issued
2019
Sprache
English
Author(s)
Herausgeber*innen
Institut
TORE-URI
Journal
Volume
119
Start Page
233
End Page
258
Citation
Banach Center Publications (119): 233-258 (2019)
Contribution to Conference
Publisher DOI
ArXiv ID
Publisher
Inst.
We study spaces CVk(Ω,E) of k-times continuously partially differentiable functions on an open set Ω⊂Rd with values in a locally convex Hausdorff space E. The space CVk(Ω,E) is given a weighted topology generated by a family of weights Vk. For the space CVk(Ω,E) and its subspace CVk0(Ω,E) of functions that vanish at infinity in the weighted topology we try to answer the question whether their elements can be approximated by functions with values in a finite dimensional subspace. We derive sufficient conditions for an affirmative answer to this question using the theory of tensor products.
Subjects
approximation property
tensor product
differentiable
weight
vector-valued
DDC Class
510: Mathematik