Harmonic Operators of Ergodic Quantum Group Actions
  In this paper we study the harmonic elements of (convolution) Markov maps associated to (ergodic) actions of locally compact quantum groups on ($\sigma$-finite) von Neumann algebras. We give several equivalent conditions under which the harmonic elements are trivial. 
Massoud Amini, Mehrdad Kalantar and Mohammad S. M. Moakhar
math.OA