Continuous functions over a pure C*-algebra
Abstract
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.
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Banach Space Theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 16 February 2026
- Language
- EN
- Document type
- Preprint