The approximation property for weighted spaces of differentiable functions

Publikationstyp
Journal Article
Publikationsdatum
2019
Sprache
English
Author
Kruse, Karsten 
Herausgeber*innen
Institute of Mathematics of the Polish Academy of Sciences 
Institut
Mathematik E-10 
TORE-URI
http://hdl.handle.net/11420/7800
Enthalten in
Banach Center Publications 
Volume
119
Start Page
233
End Page
258
Citation
Banach Center Publications (119): 233-258 (2019)
Contribution to Conference
12th International Conferences on Function Spaces, 2018 
Publisher DOI
10.4064/bc119-14
ArXiv ID
1806.02926
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.
Schlagworte
approximation property
tensor product
differentiable
weight
vector-valued
DDC Class
510: Mathematik