Lieb–Thirring Inequalities for Jacobi Matrices Original Research Article

For a Jacobi matrix J on ℓ2(Z+) with Ju(n)=an−1u(n−1)+bnu(n)+anu(n+1), we prove that∑∣E∣>2(E2−4)1/2⩽∑n∣bn∣+4∑n∣an−1∣. We also prove bounds on higher moments and some related results in higher dimension.