Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 2: 287 - 300

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

RESEARCH ARTICLE

Some results for operators on a model space

  • Mehmet GÜRDAL , 1 ,
  • Ula¸s YAMANCI 2 ,
  • Mübariz GARAYEV 3
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  • 1. Suleyman Demirel University, Department of Mathematics, 32260, Isparta, Turkey
  • 2. Suleyman Demirel University, Department of Statistics, 32260, Isparta, Turkey
  • 3. Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Received date: 17 Mar 2017

Accepted date: 12 Feb 2018

Published date: 28 Mar 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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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 Kθ = 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.

Key words： Reproducing kernel Hilbert space (RKHS); reproducing kernel; Berezin symbol; Berezin number; truncated Toeplitz operator; model operator; Toeplitz operator

Cite this article

Mehmet GÜRDAL , Ula¸s YAMANCI , Mübariz GARAYEV . Some results for operators on a model space[J]. Frontiers of Mathematics in China, 2018 , 13(2) : 287 -300 . DOI: 10.1007/s11464-018-0690-3

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