Remarks on complex symmetric Toeplitz operators

In this paper, we give an alternative characterization of complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we prove that a block Toeplitz operator (Formula presented.) is complex symmetric with the conjugation (Formula presented.) on the vector-valued Hardy space (Formula presented.) if and only if (Formula presented.), where (Formula presented.) denotes the multiplication operator on (Formula presented.) with symbol Φ. As some applications, we provide examples of normal (resp., non-normal) complex symmetric block Toeplitz operators.