Characterization of C-symmetric Toeplitz operators for a class of conjugations in Hardy spaces

In this article, we introduce a new class of conjugations in the scalar-valued Hardy space H-C(2)(D) and provide a characterization of a complex symmetric Toeplitz operator T-phi with respect to these newly introduced conjugations in various cases. Moreover, we obtain a characterization of a complex symmetric block Toeplitz operator T-Phi on the vector-valued Hardy space H-C(22)(D) with respect to certain conjugations introduced in [Camara MC, Klis-Garlicka K, Ptak M. Complex symmetric completions of partial operator matrices. Linear and Multilinear Algebra. 2019; DOI: 10.1080/03081087.2019.1631246], [Kang D, Ko E, Lee JE. Remarks on complex symmetric Toeplitz operators. Linear Multilinear Algebra. 2020; DOI: 10.1080/03081087.2020.1842847], [Ko E, Lee JE. Remark on complex symmetric operator matrices. Linear Multilinear Algebra. 2019;67(6):1198-1216].

Automated summary

This article introduces a new class of conjugations and provides characterization of complex symmetric Toeplitz operators. Moreover, a characterization of complex symmetric block Toeplitz operators is obtained.