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Ranks of commutators of Toeplitz operators on the harmonic Bergman space

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Abstract

We study the rank of commutators of two Toeplitz operators on the harmonic Bergman space of the unit disk. We first show that the commutator of any two Toeplitz operators with general symbols can’t have an odd rank. But, given any integer n ≥ 0, we also show that there are two symbols for which the corresponding Toeplitz operators induce the commutator with rank 2n exactly.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yong Chen

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

    Hyungwoon Koo

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

    Young Joo Lee

Authors
  1. Yong Chen
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  2. Hyungwoon Koo
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  3. Young Joo Lee
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Corresponding author

Correspondence to Young Joo Lee.

Additional information

The first author was supported in part by ZJNSFC (No. Y6110260), NSFC (No. 11201274) and Tianyuan Foundation of China (No. 11126259) and the second author is support by NRF of Korea (2012R1A1A2000705). Also, the third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012-0001416).

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Chen, Y., Koo, H. & Lee, Y.J. Ranks of commutators of Toeplitz operators on the harmonic Bergman space. Integr. Equ. Oper. Theory 75, 31–38 (2013). https://doi.org/10.1007/s00020-012-2020-6

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  • DOI: https://doi.org/10.1007/s00020-012-2020-6

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