Characterization of C-Symmetric Toeplitz operators for a Class of Conjugations in Hardy Spaces

Abstract

In this article, we introduce a new class of conjugations in the scalar valued Hardy space $H_{\mathbb{C}}^2(\mathbb{D})$ and provide a characterization of a complex symmetric Toeplitz operator $T_{\varphi }$ 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 $\hdct$ with respect to certain conjugations introduced in \cite{CamaGP,KangKoLee,LeeKo2019}.

Preliminary Version