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Recent Developments in the Interplay Between Function Theory and Operator Theory for Block Toeplitz, Hankel, and Model Operators

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Function Spaces, Theory and Applications

Part of the book series: Fields Institute Communications ((FIC,volume 87))

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Abstract

This is a semi-expository paper on some recent developments in the interplay between function theory and operator theory in the context of Toeplitz, Hankel, and model operators. We place special emphasis on the connections with the Beurling-Lax-Halmos Theorem, which characterizes the shift-invariant subspaces of the vector-valued Hardy space.

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Acknowledgements

The authors are grateful to the referee for a careful reading of the manuscript and for many valuable suggestions that helped improved the presentation. The work of the second named author was supported by NRF (Korea) grant No. 2019R1A2C1005182. The work of the third named author was supported by NRF (Korea) grant No. 2021R1A2C1005428.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Iowa, Iowa, IA, USA

    Raúl E. Curto

  2. Department of Mathematics, Sungkyunkwan University, Suwon, Korea

    In Sung Hwang

  3. Department of Mathematics and RIM, Seoul National University, Seoul, Korea

    Woo Young Lee

Authors
  1. Raúl E. Curto
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  2. In Sung Hwang
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  3. Woo Young Lee
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Correspondence to Raúl E. Curto .

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Editors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, Canada

    Ilia Binder

  2. Department of Mathematics and Statistics, Laval University, Québec City, QC, Canada

    Damir Kinzebulatov

  3. Department of Mathematics and Statistics, Laval University, Québec City, QC, Canada

    Javad Mashreghi

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Curto, R.E., Hwang, I.S., Lee, W.Y. (2023). Recent Developments in the Interplay Between Function Theory and Operator Theory for Block Toeplitz, Hankel, and Model Operators. In: Binder, I., Kinzebulatov, D., Mashreghi, J. (eds) Function Spaces, Theory and Applications. Fields Institute Communications, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-031-39270-2_10

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