When do Toeplitz and Hankel operators commute? (Q1583711)

The author shows that non-trivial Toeplitz (\(T_\psi\)) and Hankel (\(H_\varphi\)) operators commute if and only if the symbol \(\varphi\) of Hankel operator is \(z\psi (z)\), where \(\psi(z)=a\xi (z)+b\), \(a\neq 0\) and \(\xi (z)\) is the characteristic function of certain ``anti-symmetric'' sets of the unit circle.