This paper aims to study when a Toeplitz operator \(T_\varphi \) on the Hardy space \(H^2\) of the unit disk is complex symmetric, that is, \(T_\varphi \) admits a symmetric matrix representation relative to some orthonormal basis of \(H^2\). For certain trigonometric symbols \(\varphi \), we give necessary and sufficient conditions for \(T_\varphi \) to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”.

中文翻译：

---

复对称Toeplitz算子

本文旨在研究单位圆盘的Hardy空间\（H ^ 2 \）上的Toeplitz算子\（T_ \ varphi \）是复对称的，即\（T_ \ varphi \）接受对称矩阵表示相对于\（H ^ 2 \）的某些正交基础。对于某些三角符号\（\ varphi \），我们给出\（T_ \ varphi \）为复杂对称的充要条件。特别是，我们证明了它们的复杂对称性与“其转置的单位等效性”性质相吻合。