Stone-Weierstra{\ss} Theorems for Riesz Ideals of Continuous Functions
Functional Analysis
2021-08-20 v2
Abstract
Notions of convergence and continuity specifically adapted to Riesz ideals I of the space of continuous real-valued functions on a Lindel\"of locally compact Hausdorff space are given, and used to prove Stone-Weierstra{\ss}-type theorems for I. As applications, sufficient conditions are discussed that guarantee that various types of positive linear maps on I are uniquely determined by their restriction to various point-separating subsets of I. A very special case of this is the characterization of the strong determinacy of moment problems, which is rederived here in a rather general setting and without making use of spectral theory.
Keywords
Cite
@article{arxiv.1811.04882,
title = {Stone-Weierstra{\ss} Theorems for Riesz Ideals of Continuous Functions},
author = {Matthias Schötz},
journal= {arXiv preprint arXiv:1811.04882},
year = {2021}
}