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arXiv · 2609.40189

Convergence of spectral smoothings from compact quantum group actions

Trevor Camper·Dimitrios Giannakis·Gage Hoefer
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Abstract

In this note, we study complete and quantum Gromov-Hausdorff convergence of operator systems obtained using smoothings of C*-algebras, where our smoothings arise from the action of a compact quantum group on the C*-algebra. Specifically, we show how if $\mathbb{G}$ is a co-amenable compact quantum group acting on unital C*-algebra $\mathcal{A}$, and both are equipped with suitable quantum metrics, bounded approximate identities in $L^{1}(\mathbb{G})$ may be used for approximations of the original space $\mathcal{A}$ under the complete and quantum Gromov-Hausdorff distance. We finish by presenting some applications to the convergence of spectral truncations of compact groups and connections to previous results.

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Trevor Camper, Dimitrios Giannakis, Gage Hoefer. 2026-09-30. Convergence of spectral smoothings from compact quantum group actions. https://arxiv.org/abs/2609.40189

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