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Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach

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Abstract

For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint operators. We discuss main properties of these representation and, especially, describe relations between properties of the spectral function of Toeplitz operators in the spectral representation and properties of the symbols.

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Authors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Grigori Rozenblum

  2. The Euler International Mathematical Institute and St.Petersburg State University, Saint Petersburg, Russia

    Grigori Rozenblum

  3. Mathematics Center Sirius University of Science and Technology, Sochi, Russia

    Grigori Rozenblum

  4. Department of Mathematics, CINVESTAV, Mexico City, Mexico

    Nikolai Vasilevski

Authors
  1. Grigori Rozenblum
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  2. Nikolai Vasilevski
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Correspondence to Nikolai Vasilevski.

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G.R. was supported by the grant of the Russian Fund of Basic Research 20-01-00451.

N.V. was partially supported by CONACYT grants 280732 and FORDECYT-PRONACES/61517/2020238630, Mexico.

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Rozenblum, G., Vasilevski, N. Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach. Integr. Equ. Oper. Theory 94, 27 (2022). https://doi.org/10.1007/s00020-022-02706-3

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  • DOI: https://doi.org/10.1007/s00020-022-02706-3

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