Separation properties for positive-definite functions on locally compact quantum groups and for associated von Neumann algebras

• Jacek Krajczok ^[1] ; Adam Skalski ^[2]
  1. [1] University of Glasgow

     University of Glasgow

     Reino Unido

     
  2. [2] Institute of Mathematics

     Institute of Mathematics

     Warszawa, Polonia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01039-4
• Enlaces
  • Texto completo
• Resumen

  • Using the Godement mean on the Fourier-Stieltjes algebra of a locally compact quantum group we obtain strong separation results for quantum positive-definite functions associated to a subclass of representations, strengthening, for example, the known relationship between amenability of a discrete quantum group and existence of a net of finitely supported quantum positive-definite functions converging pointwise to 1. We apply these results to show that von Neumann algebras of unimodular discrete quantum groups enjoy a strong form of non-w∗-CPAP, which we call the matrix εseparation property.

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