Bulletin of the Korean Mathematical Society (대한수학회보)

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A SUFFICIENT CONDITION FOR HYPONORMAL TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Sumin Kim (Department of Mathematics and Institute of Basic Sciences Sungkyunkwan University) ;
  • Jongrak Lee (Department of Mathematics Sungkyunkwan University)
  • Received : 2023.09.26
  • Accepted : 2023.12.18
  • Published : 2024.07.31
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Abstract

In this paper we consider the sufficient condition for hyponormal Toeplitz operators T𝛗 with non-harmonic symbols $${\varphi}(z)=\sum_{\ell=1}^{k}{\alpha}_{\ell}z^{{m_{\ell}}{\bar{z}}n_{\ell}}$$ with mℓ-nℓ = δ > 0 for all 1 ≤ ℓ ≤ k, and αℓ ∈ ℂ on the Bergman spaces. In particular, we will observe the characteristics of the hyponormality of the Toeplitz operators T𝛗 according to the positional relationship of the coefficients αℓ's.

Keywords

Acknowledgement

The first author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(No. RS-2023-00244646). The second author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(No. 2021R1C1C1008713).

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