APPROXIMATION IN BANACH ALGEBRAS OF VECTOR-VALUED FUNCTION SPACES

Author(s):

Kobra Esmaeili*

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

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)..

Keywords:

Vector-valued Lipschitz space , Continuously differentiable vector-valued func- tion , Vector-valued measure , Approximation

Language:
Persian
Published:
Journal of Mathematical Researches, Volume:7 Issue: 2, 2021
Pages:
191 to 200
https://magiran.com/p2310262