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Invertibility and Fredholm Property of Fock Toeplitz Operators

Author

Listed:
  • Chunxu Xu

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

  • Tao Yu

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

Abstract

We characterize some necessary and sufficient conditions of invertible Toeplitz operators acting on the Fock space. In particular, we study the Fredholm properties of Toeplitz operators with B M O 1 symbols, where their Berezin transforms are bounded functions of vanishing oscillation. We show the Fredholm index of the Toeplitz operator via the winding of its Berezin transform along a sufficiently large circle and provide a characterization of invertible Toeplitz operators with non-negative symbols, possibly unbounded, such that the Berezin transforms of the symbols are bounded and of vanishing oscillation.

Suggested Citation

  • Chunxu Xu & Tao Yu, 2023. "Invertibility and Fredholm Property of Fock Toeplitz Operators," Mathematics, MDPI, vol. 11(13), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2976-:d:1186189
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    References listed on IDEAS

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    1. Nina Zorboska, 2003. "Toeplitz operators with BMO symbols and the Berezin transform," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-17, January.
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