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The spectrum of Bergman Toeplitz operators with some harmonic symbols

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Abstract

In this paper, we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and \(\bar z\) equals the image of closed unit disk under the symbol. Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and \(\bar z\).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    XianFeng Zhao

  2. Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China

    XianFeng Zhao

  3. Center of Mathematics, Chongqing University, Chongqing, 401331, China

    DeChao Zheng

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

    DeChao Zheng

Authors
  1. XianFeng Zhao
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  2. DeChao Zheng
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Correspondence to XianFeng Zhao.

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Zhao, X., Zheng, D. The spectrum of Bergman Toeplitz operators with some harmonic symbols. Sci. China Math. 59, 731–740 (2016). https://doi.org/10.1007/s11425-015-5083-4

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  • DOI: https://doi.org/10.1007/s11425-015-5083-4

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