Co-amenability of compact quantum groups

We study the concept of co-amenability for a compact quantum group. Several conditions arc derived that are shown to be equivalent to it. Some consequ ences of co-amenability that we obtain are faithfulness of the Haar integra l and automatic norm-boundedness of positive linear functionals on the quan tum group's Hopf *-algebra (neither of these properties necessarily holds w ithout co-amenability). (C) 2001 Elsevier Science B.V. All rights reserved.