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Products of Bergman space Toeplitz operators on the polydisk

Authors:	Boo Rim Choe Young Joo Lee Kyesook Nam Dechao Zheng

Institution:	(1) Department of Mathematics, Korea University, Seoul, 136-701, Korea;(2) Department of Mathematics, Chonnam National University, Gwangju, 500-757, Korea;(3) Department of Mathematics, Hanshin University, Gyeonggi, 447-791, Korea;(4) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA

Abstract:	Motivated by recent works of Ahern and $\breve{\rm C}$ u $\breve{\rm C}$ ković on the disk, we study the generalized zero product problem for Toeplitz operators acting on the Bergman space of the polydisk. First, we extend the results to the polydisk. Next, we study the generalized compact product problem. Our results are new even on the disk. As a consequence on higher dimensional polydisks, we show that the generalized zero and compact product properties are the same for Toeplitz operators in a certain case.The first three authors were partially supported by KOSEF(R01-2003-000-10243-0) and the last author was partially supported by the National Science Foundation.

Keywords:	Primary 47B35 Secondary 32A36
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