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Algebraic Properties of Toeplitz Operators on the Harmonic Dirichlet Space

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Abstract

We study some algebraic properties of Toeplitz operators on the harmonic Dirichlet space of the unit disk. We first give a characterization for boundedness of Toeplitz operators. Next we characterize commuting Toeplitz operators. Also, we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. The corresponding problems for compactness are also studied.

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Authors and Affiliations

  1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, 321004, Jinhua, People’s Republic of China

    Yong Chen

  2. School of Mathematical Sciences, Fudan University, 200433, Shanghai, People’s Republic of China

    Yong Chen

  3. Department of Mathematics, Chonnam National University, Gwangju, 500-757, Korea

    Young Joo Lee

  4. Department of Mathematics, Ha Noi National University of Education, 136 Xuan Thuy, Ha Noi, Vietnam

    Quang Dieu Nguyen

Authors
  1. Yong Chen
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  2. Young Joo Lee
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  3. Quang Dieu Nguyen
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Corresponding author

Correspondence to Young Joo Lee.

Additional information

Y. Chen is supported by NNSFC (No. 10971195) and ZJNSFC (No. Y6090689).

Q. D. Nguyen was supported by the NAFOSTED program.

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Chen, Y., Lee, Y.J. & Nguyen, Q.D. Algebraic Properties of Toeplitz Operators on the Harmonic Dirichlet Space. Integr. Equ. Oper. Theory 69, 183–201 (2011). https://doi.org/10.1007/s00020-010-1822-7

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  • DOI: https://doi.org/10.1007/s00020-010-1822-7

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