On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrodinger operators

We study to what extent Lieb-Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schrodinger operators. Namely, we prove the conjecture of Hansmann and Katriel from [12] and answer another open question raised therein. The results are obtained by means of asymptotic analysis of eigenvalues of discrete Schrodinger operators with rectangular barrier potential and complex coupling. Applying the ideas in the continuous setting, we also solve a similar open problem for one-dimensional Schrodinger operators with complex-valued potentials published by Demuth, Hansmann, and Katriel in [5].