CONVERGENCE OF FOURIER TRUNCATIONS

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. When the truncations and the containing C*-algebra are equipped with suitable quantum metrics, then under suitable conditions the truncations converge to the containing C*-algebra for quantum Gromov-Hausdorff distance.