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Some results for operators on a model space

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Abstract

We investigate some problems for truncated Toeplitz operators. Namely, the solvability of the Riccati operator equation on the set of all truncated Toeplitz operators on the model space K θ = H2ΘθH2 is studied. We study in terms of Berezin symbols invertibility of model operators. We also prove some results for the Berezin number of the truncated Toeplitz operators. Moreover, we study some property for H2-functions in terms of noncyclicity of co-analytic Toeplitz operators and hypercyclicity of model operators.

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Acknowledgements

The authors thank the referees for their useful and constructive remarks and suggestions which improved the presentation of the paper. This work was supported by TüBA through Young Scientist Award Program (TüBA-GEB_IP/2015). Also, the third author would like to extend his sincere appreciation to the Deanship of Scientific Research at King Saudi University for funding this Research group No. RGP-VPP-323.

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Authors and Affiliations

  1. Department of Mathematics, Suleyman Demirel University, 32260, Isparta, Turkey

    Mehmet Gürdal

  2. Department of Statistics, Suleyman Demirel University, 32260, Isparta, Turkey

    Ulaş Yamanci

  3. Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia

    Mübariz Garayev

Authors
  1. Mehmet Gürdal
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  2. Ulaş Yamanci
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  3. Mübariz Garayev
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Correspondence to Mehmet Gürdal.

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Gürdal, M., Yamanci, U. & Garayev, M. Some results for operators on a model space. Front. Math. China 13, 287–300 (2018). https://doi.org/10.1007/s11464-018-0690-3

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  • DOI: https://doi.org/10.1007/s11464-018-0690-3

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