Fejér representations for discrete quantum groups and applications
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916603402125312 |
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| author | Crann, Jason Kazemi, Soroush Neufang, Matthias |
| author_facet | Crann, Jason Kazemi, Soroush Neufang, Matthias |
| contents | We prove that a discrete quantum group $\mathbb{G}$ has the approximation property if and only if a Fejér-type representation holds for its $C^*$-algebraic or von Neumann algebraic crossed products. As applications, we extend several results from the literature to the context of discrete quantum groups with the approximation property. Additionally, we provide new characterizations of invariant $L^\infty(\widehat{\mathbb{G}})$-bimodules of $\mathcal{B}(\ell^2(\mathbb{G}))$ and invariant $C(\widehat{\mathbb{G}})$-bimodules of $\mathcal{K}(\ell^2(\mathbb{G}))$, some of which are new in the group setting. Finally, we study Fubini crossed products of discrete quantum group actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fejér representations for discrete quantum groups and applications Crann, Jason Kazemi, Soroush Neufang, Matthias Operator Algebras Functional Analysis We prove that a discrete quantum group $\mathbb{G}$ has the approximation property if and only if a Fejér-type representation holds for its $C^*$-algebraic or von Neumann algebraic crossed products. As applications, we extend several results from the literature to the context of discrete quantum groups with the approximation property. Additionally, we provide new characterizations of invariant $L^\infty(\widehat{\mathbb{G}})$-bimodules of $\mathcal{B}(\ell^2(\mathbb{G}))$ and invariant $C(\widehat{\mathbb{G}})$-bimodules of $\mathcal{K}(\ell^2(\mathbb{G}))$, some of which are new in the group setting. Finally, we study Fubini crossed products of discrete quantum group actions. |
| title | Fejér representations for discrete quantum groups and applications |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2502.05125 |