Some results for operators on a model space

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

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Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature