The tracial Rokhlin property for an inclusion of unital $C^*$-algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866916239527378944 |
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| author | Lee, Hyun Ho Osaka, Hiroyuki |
| author_facet | Lee, Hyun Ho Osaka, Hiroyuki |
| contents | We introduce and study a notion of Rokhlin property for an inclusion of unital $C^*$-algebras which could have no projections like the Jiang-Su algebra. We also introduce a notion of approximate representability and show a duality between them. We demonstrate the importance of these notions by showing the permanence of the tracial $\mathcal{Z}$-absorbingness and the strict comparison property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_01613 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The tracial Rokhlin property for an inclusion of unital $C^*$-algebras Lee, Hyun Ho Osaka, Hiroyuki Operator Algebras 46L35, 47C15, 46L55 We introduce and study a notion of Rokhlin property for an inclusion of unital $C^*$-algebras which could have no projections like the Jiang-Su algebra. We also introduce a notion of approximate representability and show a duality between them. We demonstrate the importance of these notions by showing the permanence of the tracial $\mathcal{Z}$-absorbingness and the strict comparison property. |
| title | The tracial Rokhlin property for an inclusion of unital $C^*$-algebras |
| topic | Operator Algebras 46L35, 47C15, 46L55 |
| url | https://arxiv.org/abs/1805.01613 |