Abstract
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”.
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