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Abstract
In this paper, we develop a machinery to study multiplication operators on the Bergman space via the Hardy space of the bidisk. Using the machinery we study the structure of reducing subspaces of a multiplication operator on the Bergman space. As a consequence, we completely classify reducing subspaces of the multiplication operator by a Blaschke product φ with order three on the Bergman space to solve a conjecture of Zhu [J. London Math. Soc. 62: 553–568, 2000].
Received: 2006-08-11
Revised: 2007-12-20
Published Online: 2009-01-21
Published in Print: 2009-March
© Walter de Gruyter Berlin · New York 2009
