|Publisher DOI:||10.4064/bc119-14||Title:||The approximation property for weighted spaces of differentiable functions||Language:||English||Authors:||Kruse, Karsten||Editor:||Institute of Mathematics of the Polish Academy of Sciences||Keywords:||approximation property;tensor product;differentiable;weight;vector-valued||Issue Date:||2019||Publisher:||Inst.||Source:||Banach Center Publications (119): 233-258 (2019)||Abstract (english):||
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.
|Conference:||12th International Conferences on Function Spaces, 2018||URI:||http://hdl.handle.net/11420/7800||ISSN:||1730-6299||Institute:||Mathematik E-10||Document Type:||Article||Journal:||Banach Center Publications|
|Appears in Collections:||Publications without fulltext|
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