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arXiv · 2602.14809

Continuous functions over a pure C*-algebra

Apurva Seth·Eduard Vilalta
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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.

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Apurva Seth, Eduard Vilalta. 2026-02-16. Continuous functions over a pure C*-algebra. https://arxiv.org/abs/2602.14809

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