Remarks on complex symmetric Toeplitz operators

Abstract

ABSTRACT 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 is complex symmetric with the conjugation on the vector-valued Hardy space if and only if , where denotes the multiplication operator on with symbol Φ. As some applications, we provide examples of normal (resp., non-normal) complex symmetric block Toeplitz operators.