Hyperlinearity via amenable near representations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914233532284928 |
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| author | Kahl, Paula Schneider, Friedrich Martin |
| author_facet | Kahl, Paula Schneider, Friedrich Martin |
| contents | We note a characterization of the amenability of unitary representations (in the sense of Bekka) via the existence of an orthonormal basis supporting an invariant probability charge. Based on this, we explore several natural notions of amenable near representations on Hilbert spaces. Establishing an analogue of a theorem about sofic groups by Elek and Szabó, we prove that a group is hyperlinear if and only if it admits an essentially free amenable near representation. This answers a question raised by Pestov and Kwiatkowska. For comparison, we also provide characterizations of Kirchberg's factorization property, as well as Haagerup's property, along similar lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperlinearity via amenable near representations Kahl, Paula Schneider, Friedrich Martin Group Theory Functional Analysis 22D10, 20P05, 47A20, 22D55 We note a characterization of the amenability of unitary representations (in the sense of Bekka) via the existence of an orthonormal basis supporting an invariant probability charge. Based on this, we explore several natural notions of amenable near representations on Hilbert spaces. Establishing an analogue of a theorem about sofic groups by Elek and Szabó, we prove that a group is hyperlinear if and only if it admits an essentially free amenable near representation. This answers a question raised by Pestov and Kwiatkowska. For comparison, we also provide characterizations of Kirchberg's factorization property, as well as Haagerup's property, along similar lines. |
| title | Hyperlinearity via amenable near representations |
| topic | Group Theory Functional Analysis 22D10, 20P05, 47A20, 22D55 |
| url | https://arxiv.org/abs/2504.10988 |