Volume 7, Issue 2 (Vol.7, No. 2, 2021)
mmr 2021, 7(2): 191-200 |
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Esmaeili K. APPROXIMATION IN BANACH ALGEBRAS OF VECTOR-VALUED FUNCTION SPACES. mmr 2021; 7 (2) :191-200
URL: http://mmr.khu.ac.ir/article-1-2977-en.html
URL: http://mmr.khu.ac.ir/article-1-2977-en.html
Faculty of Engineering, Ardakan University, Ardakan, Iran , esmaeili@ardakan.ac.ir
Abstract: (1416 Views)
In this paper, we give a criterion for the density of a subspace of lip _{alpha} (X; S)
when (X; d) is a compact metric space, S is a complex Banach space and 0 < alpha< 1.
In the case where X = [a; b], we conclude that Lip1(X; S) is dense in lip _{alpha}(X; S). Also,
using Bochner spaces and the duality we show that C1([a; b]; S), the space of continuously
differentiable S-valued functions on [a; b], is dense in lip _{alpha} ([a; b]; S)../files/site1/files/72/2Abstract.pdf
when (X; d) is a compact metric space, S is a complex Banach space and 0 < alpha< 1.
In the case where X = [a; b], we conclude that Lip1(X; S) is dense in lip _{alpha}(X; S). Also,
using Bochner spaces and the duality we show that C1([a; b]; S), the space of continuously
differentiable S-valued functions on [a; b], is dense in lip _{alpha} ([a; b]; S)../files/site1/files/72/2Abstract.pdf
Keywords: Vector-valued Lipschitz space, Continuously differentiable vector-valued func- tion, Vector-valued measure, Approximation.
Type of Study: S |
Subject:
alg
Received: 2019/07/12 | Revised: 2021/08/7 | Accepted: 2019/11/4 | Published: 2021/09/1 | ePublished: 2021/09/1
Received: 2019/07/12 | Revised: 2021/08/7 | Accepted: 2019/11/4 | Published: 2021/09/1 | ePublished: 2021/09/1
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