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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.14809 |
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| _version_ | 1866917285522833408 |
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| author | Seth, Apurva Vilalta, Eduard |
| author_facet | Seth, Apurva Vilalta, Eduard |
| contents | Let $X$ be a compact metric space, and let $A$ be a pure $\mathrm{C}^*$-algebra. We show that $C(X,A)$ is pure whenever $A$ is simple; or every quotient of $A$ is stably finite (e.g., $A$ has stable rank one).
Using permanence properties of pureness, we prove that the tensor product of any such $A$ with any ASH-algebra is pure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14809 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Continuous functions over a pure C*-algebra Seth, Apurva Vilalta, Eduard Operator Algebras 46L05 Let $X$ be a compact metric space, and let $A$ be a pure $\mathrm{C}^*$-algebra. We show that $C(X,A)$ is pure whenever $A$ is simple; or every quotient of $A$ is stably finite (e.g., $A$ has stable rank one). Using permanence properties of pureness, we prove that the tensor product of any such $A$ with any ASH-algebra is pure. |
| title | Continuous functions over a pure C*-algebra |
| topic | Operator Algebras 46L05 |
| url | https://arxiv.org/abs/2602.14809 |