Co-Amenability of compact quantum groups
  We study the concept of co-amenability for a compact quantum group. Several conditions are derived that are shown to be equivalent to it. Some consequences of co-amenability that we obtain are faithfulness of the Haar integral and automatic norm-boundedness of positive linear functionals on the quantum group's Hopf *-algebra (neither of these properties necessarily holds without co-amenability). 
Erik Bedos, Gerard J. Murphy, Lars Tuset