On ergodic properties of convolution operators associated with compact quantum groups

TL;DR

This paper applies recent noncommutative ergodic theory results to analyze the convergence properties of convolution operators on compact quantum groups, advancing understanding in noncommutative harmonic analysis.

Contribution

It extends ergodic theorems to convolution operators on compact quantum groups, linking noncommutative L^p-space results with quantum group convolutions.

Findings

Established almost uniform convergence of convolution operators

Connected noncommutative ergodic theory with quantum group analysis

Extended classical ergodic results to the quantum setting

Abstract

Recent results of M.Junge and Q.Xu on the ergodic properties of the averages of kernels in noncommutative L^p-spaces are applied to the analysis of the almost uniform convergence of operators induced by the convolutions on compact quantum groups.