Properties of generalized Toeplitz operators (Q5943204)

Let \(H_j, j=1,2\) be the Hilbert spaces and \(T_j, j=1,2\) be two contractions defined on \(H_j\) respectively. The operator \(X: H_1\to H_2\) is called a generalized Toeplitz operator if \(X=T_2XT_1^\ast\) and a generalized Hankel operator if \(T_2X=XT_1^\ast\). The authors study which properties of classical Toeplitz and Hankel operators depend only on their generalized relations and not on the machinery of complex function theory.