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Products of Bergman space Toeplitz operators on the polydisk

Mathematische Annalen volume 337, pages 295–316 (2007)Cite this article

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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Authors and Affiliations

  1. Department of Mathematics, Korea University, Seoul, 136-701, Korea

    Boo Rim Choe

  2. Department of Mathematics, Chonnam National University, Gwangju, 500-757, Korea

    Young Joo Lee

  3. Department of Mathematics, Hanshin University, Gyeonggi, 447-791, Korea

    Kyesook Nam

  4. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Dechao Zheng

Authors
  1. Boo Rim Choe
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  2. Young Joo Lee
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  3. Kyesook Nam
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  4. Dechao Zheng
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Corresponding author

Correspondence to Dechao Zheng.

Additional information

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

Mathematics Subject Classification (2000)

  • Primary 47B35
  • Secondary 32A36