Stone-Weierstrass theorems in C*(X)

JOURNAL OF APPROXIMATION THEORY

卷:107

Article

Bustamante, J ; Montalvo, F

关键词: uniform closure;    Lebesgue sets;    chain condition;    multipliers;   

DOI  :  10.1006/jath.2000.3507

来源: Elsevier

【 摘 要 】

In this paper we consider some conditions for a given function f epsilon C*(X) to belong to the uniform closure of a subset W subset of C*(X). We start with a general theorem which admits a sensible improvement when W, or more generally its uniform closure cl( W), is a lattice. Also, we obtain an approximation result when W or cl(W) is a cone. From this result we can derive one by Blasco and Molto for linear subspaces and one by Garrido and Montalvo for semi-affine lattices. Finally, using multipliers, we extend to C*(X) some other known results for the compact case, such as the Nachbin theorem about the uniform closure of an A-module. (C) 2000 Academic Press.

【 授权许可】

Free