Invertibility of Bergman Toeplitz operators with harmonic polynomial symbols
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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.
KeywordsBergman space Toeplitz operator harmonic polynomial symbol invertibility
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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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