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Journal of Function Spaces and Applications
Volume 2013, Article ID 578436, 12 pages
Research Article

Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China

Received 20 June 2012; Revised 7 September 2012; Accepted 6 October 2012

Academic Editor: Nikolai M. Vasilevski

Copyright © 2013 Jingyu Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols.