INVARIANT SUBSPACES FOR BISHOP-TYPE OPERATORS

Nontrivial hyperinvariant subspaces are exhibited for a class of weighted translation operators which includes many operators of the form MφUα, on L2[0, 1), where φ ε{lunate} Lα[0, 1) and Uα, is translation, modulo one, by an irrational α. In particular, if φ is the restriction to [0, 1) of a function analytic in some open neighbourhood of [0, 1] in the complex plane, then MφUα has a nontrivial hyperinvariant subspace for almost all α. © 1990.