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Block dual Toeplitz Operators on the Orthogonal Complements of Fock Spaces

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Abstract

In this paper, we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces, and the compactness of the finite sum of two dual Toeplitz operators products. The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.

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References

  1. Axler, S., Čučuković, Z.: Commuting Toeplitz operators with harmonic symbols. Integr. Equ. Oper. Theory, 14, 1–11 (1991)

    Article  MathSciNet  Google Scholar 

  2. Axler, S., Čučuković, Z., Rao, N.: Commutants of analytic Toeplitz operators on the Bergman space. Proc. Amer. Math. Soc., 128, 1951–1953 (2000)

    Article  MathSciNet  Google Scholar 

  3. Brown, A., Halmos, P.: Algebraic properties of Toeplitz operators. J. Reine Angew. Math., 100, 89–102 (1963)

    MathSciNet  Google Scholar 

  4. Chen, Y., Lee, Y.: Sums of dual Toeplitz products on the orthogonal complements of the Fock spaces. Integr. Equ. Oper. Theory, 93, 1–12 (2021)

    Article  MathSciNet  Google Scholar 

  5. Chen, Y., Yu, T., Zhao, Y.: Dual Toeplitz operators on orthogonal complement of the harmonic Dirichlet space. Acta Math. Sin., Engl. Ser., 33, 1–20 (2017)

    Article  MathSciNet  Google Scholar 

  6. Gu, C., Zheng, D.: Products of block Toeplitz operators. Pacific J. Math., 185, 115–148 (1998)

    Article  MathSciNet  Google Scholar 

  7. He, L., Huang, P., Lee, Y.: Sums of dual Toeplitz products on the orthogonal complements of the Hardy–Sobolev spaces. Complex Anal. Oper. Theory, 15, 1–23 (2021)

    Article  MathSciNet  Google Scholar 

  8. Kong, L., Lu, Y.: Some algebraic properties of dual Toeplitz operators. Houston J. Math., 44, 169–185 (2018)

    MathSciNet  Google Scholar 

  9. Lu, Y., Yang, J.: Commuting dual Toeplitz operators on weighted Bergman spaces of the unit ball. Acta Math. Sin., Engl. Ser., 27, 1725–1742 (2011)

    Article  MathSciNet  Google Scholar 

  10. Rudin, W.: Real and Complex Analysis. 2nd Ed., McGraw-Hill, New York, 1974

    Google Scholar 

  11. Stroethoff, K.: Essentially commuting Toeplitz operators with harmonic symbols. Canad. J. Math., 45, 1080–1093 (1993)

    Article  MathSciNet  Google Scholar 

  12. Stroethoff, K., Zheng, D.: Algebraic and spectral properties of dual Toeplitz operators. Trans. Amer. Math. Soc., 354, 2495–2520 (2002)

    Article  MathSciNet  Google Scholar 

  13. Yang, J., Hu, Y., Lu, Y., et al.: Commuting dual Toeplitz operators on the harmonic Dirichlet space. Acta Math. Sin., Engl. Ser., 32, 1099–1105 (2016)

    Article  MathSciNet  Google Scholar 

  14. Yang, J., Lu, Y.: Commuting dual Toeplitz operators on the harmonic Bergman space. Sci. China Math., 58, 1461–1472 (2015)

    Article  MathSciNet  Google Scholar 

  15. Yang, P., Zhao, X.: Dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space. Acta Math. Sin., Engl. Ser., 37, 1143–1155 (2021)

    Article  MathSciNet  Google Scholar 

  16. Zhang, B., Lu, Y.: Commuting of block Toeplitz operators. Operators and Matrices, 8, 635–650 (2014)

    Article  MathSciNet  Google Scholar 

  17. Zhu, K.: Analysis on Fock Spaces, Springer Science+Business Media, New York, 2012

    Book  Google Scholar 

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P. R. China

    Jian Xiang Dong & Yu Feng Lu

  2. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, P. R. China

    Chun Xu Xu

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  1. Jian Xiang Dong
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  2. Chun Xu Xu
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  3. Yu Feng Lu
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Correspondence to Chun Xu Xu.

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Conflict of Interest The authors declare no conflict of interest.

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Supported by NSFC (Grant No. 12031002)

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Dong, J.X., Xu, C.X. & Lu, Y.F. Block dual Toeplitz Operators on the Orthogonal Complements of Fock Spaces. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-2587-2

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  • DOI: https://doi.org/10.1007/s10114-024-2587-2

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