Convergence of Fourier truncations for compact quantum groups and finitely generated groups

We generalize the Fejer-Riesz operator systems defined for the circle group by Connes and van Suijlekom to the setting of compact matrix quantum groups and their ergodic actions on C'-algebras. These truncations form filtrations of the containing C'-algebra. We show that when they and the containing C'-algebra are equipped with suitable quantum metrics, then under suitable conditions they converge to the containing C'-algebra for quantum Gromov-Hausdorff distance. Among other examples, our results are applicable to the quantum groups SUq(2) and their homogeneous spaces Sq2.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).