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A conjugation $C$ on a separable complex Hilbert space $\mathcal H$ is anantilinear operator that is isometric and involutive. In this notes, wecharacterize all conjugations on the Hardy-Hilbert space $H^{2}$ over the disk.In addition, we characterize complex symmetric Toeplitz operators with aspecial type of these conjugations.

Conjugations on the Hardy space $H^{2}$