Abstract. The functional calculus approach of Davie is extended to show the existence of hyperinvariant subspaces for a collection of weighted composition operators that includes certain products of Bishop operators. Moreover it is shown that such operators have trivial point spectrum.

AMS Subject Classification (1991): 47A15; 47A10, 47A60, 47A15

Received October 15, 2007, and in revised form March 21, 2008. (Registered under 6041/2009.)