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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.11983 |
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| _version_ | 1866911005402988544 |
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| author | Bouwen, Ben Pi, Jennifer |
| author_facet | Bouwen, Ben Pi, Jennifer |
| contents | We study existence of embeddings into ultrapowers of the Jiang-Su algebra $\mathcal{Z}$ and the Razak-Jacelon algebra $\mathcal{W}$. More specifically, we show that the cone over any separable $C^*$-algebra embeds into the ultrapowers of both $\mathcal{Z}$ and $\mathcal{W}$. We also show that the result for $\mathcal{Z}$ generalizes to separable and exact continuous fields of $C^*$-algebras for which one of the fibers embeds into the ultrapower of $\mathcal{Z}$, if this fiber is suitably well-behaved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embeddings into the ultrapower of the Jiang-Su algebra Bouwen, Ben Pi, Jennifer Operator Algebras 46L35 We study existence of embeddings into ultrapowers of the Jiang-Su algebra $\mathcal{Z}$ and the Razak-Jacelon algebra $\mathcal{W}$. More specifically, we show that the cone over any separable $C^*$-algebra embeds into the ultrapowers of both $\mathcal{Z}$ and $\mathcal{W}$. We also show that the result for $\mathcal{Z}$ generalizes to separable and exact continuous fields of $C^*$-algebras for which one of the fibers embeds into the ultrapower of $\mathcal{Z}$, if this fiber is suitably well-behaved. |
| title | Embeddings into the ultrapower of the Jiang-Su algebra |
| topic | Operator Algebras 46L35 |
| url | https://arxiv.org/abs/2506.11983 |