In the first paper of this series [17], we set up some general machinery for studying ergodic actions of compact groups on von Neumann algebras, namely, those actions for which . In particular we obtained a characterisation of the full multiplicity ergodic actions:
THEOREM A. If α is an ergodic action of G on , then the following conditions are equivalent:
(1) Each spectral subspace has multiplicity dim π for π in .
(2) Each π in admits a unitary eigenmatrix in .
(3) The W* crossed product is a (Type I) factor.
(4) The C* crossed product of the C* algebra of norm continuity is isomorphic to the algebra of compact operators on a Hilbert space.