Traces on the uniform tracial completion of $\mathcal{Z}$-stable C*-algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915314391842816 |
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| author | Evington, Samuel |
| author_facet | Evington, Samuel |
| contents | The uniform tracial completion of a C*-algebra A with compact non-empty trace space T(A) is obtained by completing the unit ball with respect to the uniform 2-seminorm $\|a\|_{2,T(A)}=\sup_{τ\in T(A)} τ(a^*a)^{1/2}$. The trace problem asks whether every trace on the uniform tracial completion is the $\|\cdot\|_{2,T(A)}$-continuous extension of a trace on A. We answer this question positively in the case of C*-algebras that tensorially absorb the Jiang-Su algebra, such as those studied in the Elliott classification programme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Traces on the uniform tracial completion of $\mathcal{Z}$-stable C*-algebras Evington, Samuel Operator Algebras 46L35 The uniform tracial completion of a C*-algebra A with compact non-empty trace space T(A) is obtained by completing the unit ball with respect to the uniform 2-seminorm $\|a\|_{2,T(A)}=\sup_{τ\in T(A)} τ(a^*a)^{1/2}$. The trace problem asks whether every trace on the uniform tracial completion is the $\|\cdot\|_{2,T(A)}$-continuous extension of a trace on A. We answer this question positively in the case of C*-algebras that tensorially absorb the Jiang-Su algebra, such as those studied in the Elliott classification programme. |
| title | Traces on the uniform tracial completion of $\mathcal{Z}$-stable C*-algebras |
| topic | Operator Algebras 46L35 |
| url | https://arxiv.org/abs/2407.00727 |