On the small boundary property and $\mathcal Z$-absorption

George A. Elliott; Zhuang Niu

On the small boundary property and $\mathcal Z$-absorption

Operator Algebras 2025-12-11 v2 Dynamical Systems

Authors: George A. Elliott , Zhuang Niu

Abstract

We introduce the Property (C) for a unital commutative sub-C*-algebra $D$ of a unital C*-algebra $A$ , a version of the relative comparison property using almost normalizers. Under the assumption of this property, the $\mathcal Z$ -absorption of $A$ is shown to imply the small boundary property of $(D, \mathrm{T}(A)|_D)$ , where $A =\mathrm{C}(X) \rtimes \mathbb Z^d$ and $D = \mathrm{C}(X)$ .

Keywords

c*-algebras topological properties

Cite

@article{arxiv.2504.03611,
  title  = {On the small boundary property and $\mathcal Z$-absorption},
  author = {George A. Elliott and Zhuang Niu},
  journal= {arXiv preprint arXiv:2504.03611},
  year   = {2025}
}

Comments

The original version contains a mistake in Section 3 on comparison using almost normalizers (Property (C)). In this revised version, Property (C) is used as the assumption, and we do not know if it holds for Jiang-Su absorbing C*-algebras

On the small boundary property and $\mathcal Z$-absorption

Abstract

Keywords

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