Let L be the von Neumann
algebra crossed product determined by a maximal abelian selfadjoint algebra L∞(X)
and an ergodic automorphism of L∞(X). The algebra L is generated by a bilateral
shift L and an abelian algebra ML isomorphic to L∞(X). The non selfadjoint
subalgebra L+ of L is the weakly closed algebra generated by L and ML. The
invariant subspaces of L+ are studied. The notion of multiplicity function is analysed
and it is shown that every function m with nonnegative integral values and whose
integral, over X, is not greater than the measure of X, is a multiplicity function. The
condition is also a necessary one. We also discuss the notion of canonical models in
this setting.
