Some results for operators on a model space

doi:10.1007/s11464-018-0690-3

Front. Math. China

2018, Vol. 13

Issue (2) : 287-300 https://doi.org/10.1007/s11464-018-0690-3

RESEARCH ARTICLE

Some results for operators on a model space

Mehmet GÜRDAL¹(

), Ula¸s YAMANCI², Mübariz GARAYEV³

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

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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.

Keywords Reproducing kernel Hilbert space (RKHS) reproducing kernel Berezin symbol Berezin number truncated Toeplitz operator model operator Toeplitz operator

Corresponding Author(s): Mehmet GÜRDAL

Issue Date: 28 March 2018

Cite this article:

Mehmet GÜRDAL,Ula¸s YAMANCI,Mübariz GARAYEV. Some results for operators on a model space[J]. Front. Math. China, 2018, 13(2): 287-300.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0690-3
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I2/287

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