C*-algebras of stable rank one and their Cuntz semigroups
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866909414231900160 |
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| author | Antoine, Ramon Perera, Francesc Robert, Leonel Thiel, Hannes |
| author_facet | Antoine, Ramon Perera, Francesc Robert, Leonel Thiel, Hannes |
| contents | The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: We answer affirmatively, for the class of stable rank one C*-algebras, a conjecture by Blackadar and Handelman on dimension functions, the Global Glimm Halving problem, and the problem of realizing functions on the cone of 2-quasitraces as ranks of Cuntz semigroup elements. We also gain new insights into the comparability properties of positive elements in C*-algebras of stable rank one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_03984 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | C*-algebras of stable rank one and their Cuntz semigroups Antoine, Ramon Perera, Francesc Robert, Leonel Thiel, Hannes Operator Algebras 46L05 (Primary), 06B35, 06F05, 19K14, 46L08, 46L35 (Secondary) The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: We answer affirmatively, for the class of stable rank one C*-algebras, a conjecture by Blackadar and Handelman on dimension functions, the Global Glimm Halving problem, and the problem of realizing functions on the cone of 2-quasitraces as ranks of Cuntz semigroup elements. We also gain new insights into the comparability properties of positive elements in C*-algebras of stable rank one. |
| title | C*-algebras of stable rank one and their Cuntz semigroups |
| topic | Operator Algebras 46L05 (Primary), 06B35, 06F05, 19K14, 46L08, 46L35 (Secondary) |
| url | https://arxiv.org/abs/1809.03984 |