Separation properties for positive-definite functions on locally compact quantum groups and for associated von Neumann algebras
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916582268076032 |
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| author | Krajczok, Jacek Skalski, Adam |
| author_facet | Krajczok, Jacek Skalski, Adam |
| contents | 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 $ε$-separation property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10046 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Separation properties for positive-definite functions on locally compact quantum groups and for associated von Neumann algebras Krajczok, Jacek Skalski, Adam Operator Algebras Quantum Algebra Primary 46L65, Secondary 43A35, 46L89 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 $ε$-separation property. |
| title | Separation properties for positive-definite functions on locally compact quantum groups and for associated von Neumann algebras |
| topic | Operator Algebras Quantum Algebra Primary 46L65, Secondary 43A35, 46L89 |
| url | https://arxiv.org/abs/2309.10046 |