Lieb-Thirring inequalities for Jacobi matrices (Q1867509)

Let \(\{E_n^\pm\}^{N\pm}_{n=1}\) be the simple eigenvalues of the Jacobi matrix on \(l^2(\mathbb{Z}_+)\) defined by the recurrence \[ (Ju)(n)= a_{n-1}u(n-1)+ b_nu(n)+ a_nu(n+1), \] where \(a_n>0\) and \(b_n\in\mathbb{R}\). The following bound \[ \sum_{|E|>2}(E^2-4)^{1/2} \leq\sum_n |b_n|+ 4 \sum_n |a_n-1| \] holds. Some similar results are obtained as well.