Endomorphisms of Z-absorbing C*-algebras without conditional expectations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866907777091239936 |
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| author | Sato, Yasuhiko |
| author_facet | Sato, Yasuhiko |
| contents | We construct an endomorphism of the Jiang-Su algebra $\mathcal{Z}$ which does not admit a conditional expectation. This answers a question in the testamentary homework by E. Kirchberg. As an application, it is shown that any unital separable nuclear $\mathcal{Z}$-absorbing C*-algebra is non-transportable in the Cuntz algebra $\mathcal{O}_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11068 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Endomorphisms of Z-absorbing C*-algebras without conditional expectations Sato, Yasuhiko Operator Algebras Functional Analysis 46L06, 46L35, 46L51 We construct an endomorphism of the Jiang-Su algebra $\mathcal{Z}$ which does not admit a conditional expectation. This answers a question in the testamentary homework by E. Kirchberg. As an application, it is shown that any unital separable nuclear $\mathcal{Z}$-absorbing C*-algebra is non-transportable in the Cuntz algebra $\mathcal{O}_2$. |
| title | Endomorphisms of Z-absorbing C*-algebras without conditional expectations |
| topic | Operator Algebras Functional Analysis 46L06, 46L35, 46L51 |
| url | https://arxiv.org/abs/2309.11068 |