Pure C*-algebras
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912159473074176 |
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| author | Antoine, Ramon Perera, Francesc Thiel, Hannes Vilalta, Eduard |
| author_facet | Antoine, Ramon Perera, Francesc Thiel, Hannes Vilalta, Eduard |
| contents | We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simple, non-elementary C*-algebra with a unique quasitrace and with very mild comparison is pure, and, as a result, has strict comparison. Furthermore, sufficiently non-commutative C*-algebras of stable rank one and with weak comparison are likewise pure.
We also show that adequately non-elementary C*-algebras with finite nuclear dimension are pure, which leads to the verification of the non-simple Toms-Winter conjecture for a large class of C*-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11052 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pure C*-algebras Antoine, Ramon Perera, Francesc Thiel, Hannes Vilalta, Eduard Operator Algebras 46L05 (Primary) 19K14, 46L80, 46L85 (Secondary) We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simple, non-elementary C*-algebra with a unique quasitrace and with very mild comparison is pure, and, as a result, has strict comparison. Furthermore, sufficiently non-commutative C*-algebras of stable rank one and with weak comparison are likewise pure. We also show that adequately non-elementary C*-algebras with finite nuclear dimension are pure, which leads to the verification of the non-simple Toms-Winter conjecture for a large class of C*-algebras. |
| title | Pure C*-algebras |
| topic | Operator Algebras 46L05 (Primary) 19K14, 46L80, 46L85 (Secondary) |
| url | https://arxiv.org/abs/2406.11052 |