Multiplication operators in weighted Banach (and locally convex) spaces of functions holomorphic in the unit disc are well
known. In this note we investigate the connection between power boundedness, mean ergodicity and uniform mean ergodicity of
such operators.
Mathematics Subject Classification (2000). Primary 47A35, 46E15 - Secondary 46A13, 47B38
Keywords. Weighted spaces of holomorphic functions - mean ergodic operators
José Bonet: Support of the Alexander von Humboldt Foundation and MEC and FEDER Project MTM 2007-62643 and GV project Prometeo/2008/101
are gratefully acknowledged.
Dedicated to Heinz König on the occassion of his 80th birthday
Received: 13 October 2008, Revised: 18 November 2008