Stone–Weierstrass theorems for Riesz ideals of continuous functions
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Schötz, Matthias [1]
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[1] Université Libre de Bruxelles
Université Libre de Bruxelles
Arrondissement Brussel-Hoofdstad, Bélgica
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 3, 2021, págs. 587-603
- Idioma: inglés
- DOI: 10.1007/s13348-020-00301-6
- Texto completo no disponible (Saber más ...)
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Resumen
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.
