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

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发表日期：

2025年4月16日

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Jacek Krajczok,
Adam Skalski

摘要

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 $\mathbb {1}$ $1$ . We apply these results to show that von Neumann algebras of unimodular discrete quantum groups enjoy a strong form of non- $w^*$ $w^{*}$ -CPAP, which we call the matrix $\varepsilon $ $ε$ -separation property.