Strict comparison and stable rank one
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929248388775936 |
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| author | Lin, Huaxin |
| author_facet | Lin, Huaxin |
| contents | Let $A$ be a $σ$-unital finite simple $C^*$-algebra which has strict comparison property. We show that if the canonical map $Γ$ from the Cuntz semigroup to certain lower semi-continuous affine functions is surjective, then $A$ has tracial approximate oscillation zero and stable rank one. Equivalently, if $A$ has an almost unperforated and almost divisible Cuntz semigroup, then $A$ has stable rank one and tracial approximate oscillation zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09250 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strict comparison and stable rank one Lin, Huaxin Operator Algebras Let $A$ be a $σ$-unital finite simple $C^*$-algebra which has strict comparison property. We show that if the canonical map $Γ$ from the Cuntz semigroup to certain lower semi-continuous affine functions is surjective, then $A$ has tracial approximate oscillation zero and stable rank one. Equivalently, if $A$ has an almost unperforated and almost divisible Cuntz semigroup, then $A$ has stable rank one and tracial approximate oscillation zero. |
| title | Strict comparison and stable rank one |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2301.09250 |