Stone-Weierstraß Theorems for Riesz Ideals of Continuous Functions
Abstract
Notions of convergence and continuity specifically adapted to Riesz ideals I of the space of continuous real-valued functions on a Lindelöf locally compact Hausdorff space are given, and used to prove Stone-Weierstraß-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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- 10.48550/arXiv.1811.04882
- arXiv:
- arXiv:1811.04882
- Bibcode:
- 2018arXiv181104882S
- Keywords:
-
- Mathematics - Functional Analysis;
- 46E05 (Primary);
- 46E25 (Secondary)
- E-Print:
- doi:10.1007/s13348-020-00301-6