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Properties of Toeplitz Operators on the Dirichlet Space Over the Ball

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Abstract

On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero.

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Authors and Affiliations

  1. Department of Mathematics, Dalian Maritime University, Dalian, 116024, P. R. China

    Yin Yin Hu

  2. Department of Mathematics, Dalian University of Technology, Dalian, 116024, P. R. China

    Yu Feng Lu & Liu Liu

Authors
  1. Yin Yin Hu
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  2. Yu Feng Lu
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  3. Liu Liu
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Corresponding author

Correspondence to Liu Liu.

Additional information

Supported by NSFC (Grant No. 11871131), the Fundamental Research Funds for the Central Universities (Grant No. 3132019177)

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Hu, Y.Y., Lu, Y.F. & Liu, L. Properties of Toeplitz Operators on the Dirichlet Space Over the Ball. Acta. Math. Sin.-English Ser. 35, 1617–1628 (2019). https://doi.org/10.1007/s10114-019-8437-y

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  • DOI: https://doi.org/10.1007/s10114-019-8437-y

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