Solution of the semi-infinite Toda lattice for unbounded sequences (Q1599576)

It is known that the semi-infinite Toda lattice system is equivalent to the following operator equation \[ {dL(t)\over dt}= M(t)L(t)-L(t) M(t) \tag{1} \] where \(L(t)\) and \(M(t)\) are some tridiagonal operators. The authors' goal is to present a class of unbounded single infinite sequencies \(\alpha_n, \beta_n\) such that equation (1) has a unique solution, with \(L(0)= L_*\), \(M(0)=M_*\), where \(L_*\) and \(M_*\) are given operators.