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.
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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.
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Choe, B.R., Lee, Y.J., Nam, K. et al. Products of Bergman space Toeplitz operators on the polydisk. Math. Ann. 337, 295–316 (2007). https://doi.org/10.1007/s00208-006-0034-6
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DOI: https://doi.org/10.1007/s00208-006-0034-6