The approximation property for weighted spaces of differentiable functions

Karsten Kruse

doi:10.4064/bc119-14

The approximation property for weighted spaces of differentiable functions

Karsten Kruse

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

13 Downloads (Pure)

Abstract

We study spaces CV^k(Ω,E) of k-times continuously partially differentiable functions on an open set Ω⊂R^d with values in a locally convex Hausdorff space E. The space CV^k(Ω,E) is given a weighted topology generated by a family of weights V^k. For the space CV^k(Ω,E) and its subspace CV^k₀(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.

Original language	English
Title of host publication	Function Spaces XII
Editors	Marta Kosek
Pages	233-258
Number of pages	26
DOIs	https://doi.org/10.4064/bc119-14
Publication status	Published - 1 Jan 2019
Externally published	Yes
Event	12th International Conferences on Function Spaces 2018 - Krakow, Poland Duration: 9 Jul 2018 → 14 Jul 2018 Conference number: 12

Publication series

Name	Banach center publications
Publisher	Polska Akademia Nauk
Volume	119
ISSN (Print)	0137-6934

Conference

Conference	12th International Conferences on Function Spaces 2018
Country/Territory	Poland
City	Krakow
Period	9/07/18 → 14/07/18

Keywords

approximation property
tensor product
differentiable
weight
vector-valued

Access to Document

10.4064/bc119-14Licence: CC BY

15KruseFinal published version, 480 KBLicence: CC BY

Cite this

@inproceedings{6474f98caab64f759d310249ee938fe5,

title = "The approximation property for weighted spaces of differentiable functions",

abstract = "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.",

keywords = "approximation property, tensor product, differentiable, weight, vector-valued",

author = "Karsten Kruse",

year = "2019",

month = jan,

day = "1",

doi = "10.4064/bc119-14",

language = "English",

series = "Banach center publications",

publisher = "Polska Akademia Nauk",

pages = "233--258",

editor = "Marta Kosek",

booktitle = "Function Spaces XII",

note = "12th International Conferences on Function Spaces 2018 ; Conference date: 09-07-2018 Through 14-07-2018",

}

TY - GEN

T1 - The approximation property for weighted spaces of differentiable functions

AU - Kruse, Karsten

N1 - Conference code: 12

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - approximation property

KW - tensor product

KW - differentiable

KW - weight

KW - vector-valued

U2 - 10.4064/bc119-14

DO - 10.4064/bc119-14

M3 - Conference contribution

T3 - Banach center publications

SP - 233

EP - 258

BT - Function Spaces XII

A2 - Kosek, Marta

T2 - 12th International Conferences on Function Spaces 2018

Y2 - 9 July 2018 through 14 July 2018

ER -

The approximation property for weighted spaces of differentiable functions

Abstract

Publication series

Conference

Keywords

Access to Document

Fingerprint

Cite this