Products of Toeplitz and Hankel Operators on Fock Spaces

Abstract

In this paper, we characterize bounded Toeplitz product \(T_fT_{g}\) and Hankel product \(H_f^{*}H_g\) on Fock space \(F_{\alpha }^2\) for two polynomials f and g in z and \({\overline{z}}\). As a consequence, we obtain when Toeplitz operator \(T_f\) or Hankel operator \(H_f\) with the polynomial symbol f in z and \({\overline{z}}\) is bounded.

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Correspondence to Fugang Yan.

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F. Yan: This work was partially supported by the National Natural Science Foundation of China (11531003, 11701052). The first author was also supported in part by China Scholarship Council (201706050066).

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Yan, F., Zheng, D. Products of Toeplitz and Hankel Operators on Fock Spaces. Integr. Equ. Oper. Theory 92, 22 (2020). https://doi.org/10.1007/s00020-020-02577-6

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Mathematics Subject Classification

  • Primary 47B35
  • Secondary 30H20

Keywords

  • Toeplitz operator
  • Hankel operator
  • Fock space