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Separation properties for positive-definite functions on locally compact quantum groups and for associated von Neumann algebras (2309.10046v2)
Published 18 Sep 2023 in math.OA and math.QA
Abstract: Using 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 $I$. 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 $\epsilon$-separation property.