PreprintCC BY 4.0arXiv
Convergence of spectral smoothings from compact quantum group actions
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 𝔾 is a co-amenable compact quantum group acting on unital C*-algebra 𝒜, and both are equipped with suitable quantum metrics, bounded approximate identities in L1(𝔾) may be used for approximations of the original space 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.
Related
- Recognizing convergence actions as proper isometric actions on hyperbolic spaces
- Group actions on von Neumann algebras with compact open subgroups
- Poisson actions of noncompact locally compact sofic groups have completely positive sofic entropy
- Intermediate subalgebras of cross-product von Neumann algebras arising from weakly compact actions
- From veering triangulations to convergence actions and back again
BibTeX
@misc{camper2026convergence,
title = {{Convergence of spectral smoothings from compact quantum group actions}},
author = {Trevor Camper and Dimitrios Giannakis and Gage Hoefer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40189},
eprint = {2609.40189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40189},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Convergence of spectral smoothings from compact quantum group actions
AU - Trevor Camper
AU - Dimitrios Giannakis
AU - Gage Hoefer
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40189
UR - https://arxiv.org/abs/2609.40189
AB - 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 𝔾 is a co-amenable compact quantum group acting on unital C*-algebra 𝒜, and both are equipped with suitable quantum metrics, bounded approximate identities in L^1(𝔾) may be used for approximations of the original space 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.
ER -