Resumen de Separation properties for positive-definite functions on locally compact quantum groups and for associated von Neumann algebras
Jacek Krajczok, Adam G. Skalski
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.
