Stone–Weierstrass theorems for Riesz ideals of continuous functions

• Schötz, Matthias ^[1]
  1. [1] Université Libre de Bruxelles

     Université Libre de Bruxelles

     Arrondissement Brussel-Hoofdstad, Bélgica

     
• 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 ...)
• 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.