On complex symmetric Toeplitz operators (Q890486)

Let \(\mathcal H\) denote a separable complex Hilbert space. A bounded linear operator \(T\) on \(\mathcal H\) is said to be complex symmetric if there exists a conjugation \(C\) on \(\mathcal H\) such that \(CTC=T^\ast\). Recall that a conjugation on \(\mathcal H\) is a conjugate-linear, isometric involution. In the present paper, the authors study properties of certain complex symmetric Toeplitz operators on the Hardy space \(H^2\) over the open unit disk. In particular, they give a concrete description of those Toeplitz operators which are complex symmetric relative to certain special conjugations.