  We consider compact group actions on C*- and W*- algebras. We prove results
that relate the duality property of the action (as defined in the Introduction)
with other relevant properties of the system such as the relative commutant of
the fixed point algebras being trivial (called the irreducibility of the
inclusion) and also to the Galois correspondence between invariant
C*-subalgebras containing the fixed point algebra and the class of closed
normal subgroups of the compact group.
