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arXiv · 1811.04882

Stone-Weierstraß Theorems for Riesz Ideals of Continuous Functions

Matthias Schötz
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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.

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Matthias Schötz. 2019-02-20. Stone-Weierstraß Theorems for Riesz Ideals of Continuous Functions. https://doi.org/10.1007/s13348-020-00301-6

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