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Invertibility of Bergman Toeplitz operators with harmonic polynomial symbols

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Abstract

Let p be an analytic polynomial on the unit disk. We obtain a necessary and sufficient condition for Toeplitz operators with the symbol \(\overline z + p\) to be invertible on the Bergman space when all coefficients of p are real numbers. Furthermore, we establish several necessary and sufficient, easy-to-check conditions for Toeplitz operators with the symbol \(\overline z + p\) to be invertible on the Bergman space when some coefficients of p are complex numbers.

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Acknowledgements

The first author was supported by the Yunnan Natural Science Foundation (Grant No. 201601YA00004). The second author was supported by National Natural Science Foundation of China (Grant No. 11701052), Chongqing Natural Science Foundation (Grant No. cstc2017jcyjAX0373) and the Fundamental Research Funds for the Central Universities (Grant Nos. 106112016CDJRC000080 and 106112017CDJXY100007). The authors thank the reviewers for providing constructive comments and suggestions in improving the contents of this paper. The authors are grateful to Professor Dechao Zheng for various valuable discussion.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chuxiong Normal University, Chuxiong, 675000, China

    Nanxing Guan

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

    Xianfeng Zhao

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  1. Nanxing Guan
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  2. Xianfeng Zhao
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Correspondence to Xianfeng Zhao.

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Guan, N., Zhao, X. Invertibility of Bergman Toeplitz operators with harmonic polynomial symbols. Sci. China Math. 63, 965–978 (2020). https://doi.org/10.1007/s11425-018-9469-1

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  • DOI: https://doi.org/10.1007/s11425-018-9469-1

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