Journal of Operator Theory

Volume 59, Issue 2, Spring 2008 pp. 435-454.

Multiplication operators on the Bergman space and weighted shifts

Authors: Shunhua Sun (1), Dechao Zheng (2), and Changyong Zhong (3)
Author institution: (1) Institute of Mathematics, Jiaxing University, Jiaxing, Zhejiang, 314001, P. R. China
(2) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
(3) Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA

Summary: In this paper we show that the multiplication operator on the Bergman space is unitarily equivalent to a weighted unilateral shift operator of finite multiplicity if and only if its symbol is a constant multiple of the $N$-th power of a M\"obius transform.

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