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Ranks of commutators for a class of truncated Toeplitz operators

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Abstract

We consider truncated Toeplitz operators acting on infinite dimensional model spaces. We then describe the kernels and ranks of commutators of truncated Toeplitz operators with symbols induced by certain inner functions. Our results generalize recent results of Chen et al. [Oper Matrices (to appear)] to infinite dimensional model spaces.

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Acknowledgements

The authors would like to thank the referees for many helpful comments and suggestions, especially for kindly providing the second proof of Corollary 3.5. The first author was supported by NSFC (11771401) and the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01041943).

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121, People’s Republic of China

    Yong Chen & Yile Zhao

  2. Department of Mathematics, Chonnam National University, Gwangju, 61186, South Korea

    Young Joo Lee

Authors
  1. Yong Chen
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  2. Young Joo Lee
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  3. Yile Zhao
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Corresponding author

Correspondence to Young Joo Lee.

Additional information

Communicated by Jan Stochel.

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Chen, Y., Lee, Y.J. & Zhao, Y. Ranks of commutators for a class of truncated Toeplitz operators. Banach J. Math. Anal. 15, 16 (2021). https://doi.org/10.1007/s43037-020-00104-8

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  • DOI: https://doi.org/10.1007/s43037-020-00104-8

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