Real rank of extensions of C*-algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910378936500224 |
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| author | Thiel, Hannes |
| author_facet | Thiel, Hannes |
| contents | Given a closed ideal $I$ in a C*-algebra $A$, we develop techniques to bound the real rank of $A$ in terms of the real ranks of $I$ and $A/I$. Building on work of Brown, Lin and Zhang, we obtain complete solutions if $I$ belongs to any of the following classes:
(1) C*-algebras with real rank zero, stable rank one and vanishing $K_1$-group; (2) simple, purely infinite C*-algebras; (3) simple, $\mathcal{Z}$-stable C*-algebras with real rank zero; (4) separable, stable C*-algebras with an approximate unit of projections and the Corona Factorization Property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03403 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Real rank of extensions of C*-algebras Thiel, Hannes Operator Algebras Primary 46L05, 46L85, Secondary 46L45, 46M20 Given a closed ideal $I$ in a C*-algebra $A$, we develop techniques to bound the real rank of $A$ in terms of the real ranks of $I$ and $A/I$. Building on work of Brown, Lin and Zhang, we obtain complete solutions if $I$ belongs to any of the following classes: (1) C*-algebras with real rank zero, stable rank one and vanishing $K_1$-group; (2) simple, purely infinite C*-algebras; (3) simple, $\mathcal{Z}$-stable C*-algebras with real rank zero; (4) separable, stable C*-algebras with an approximate unit of projections and the Corona Factorization Property. |
| title | Real rank of extensions of C*-algebras |
| topic | Operator Algebras Primary 46L05, 46L85, Secondary 46L45, 46M20 |
| url | https://arxiv.org/abs/2311.03403 |