Continuous functions over a pure C*-algebra

Apurva Seth; Eduard Vilalta

Continuous functions over a pure C*-algebra

Operator Algebras 2026-02-24 v2

Authors: Apurva Seth , Eduard Vilalta

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.

Keywords

c*-algebras function theory general topology

Cite

@article{arxiv.2602.14809,
  title  = {Continuous functions over a pure C*-algebra},
  author = {Apurva Seth and Eduard Vilalta},
  journal= {arXiv preprint arXiv:2602.14809},
  year   = {2026}
}

Comments

19 pages; added Corollary C on strict comparison for groups of the form GxH with G acylindrically hyperbolic and H virtually abelian

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