Toeplitz operators and Hankel operators (Q5906452)

In the paper [\textit{B. A. Lotto}, J. Oper. Theory 24, No. 1, 17-22 (1990; Zbl 0774.47011)] the following result was proved: if \(T_ \varphi\), \(H_ \psi\) are correspondingly Toeplitz and Hankel operators on Hardy space \(H^ 2(T)\) and \(R(T_ \varphi)\subset R(T_ \psi)\) then \(T_ \varphi=0\). The author extends this result on the Toeplitz and Hankel operators related with shifts in Hilbert space.