We consider C = A + B where A is selfadjoint with a gap (a, b) in its spectrum and B is (relatively) compact. We prove a general result allowing B of indefinite sign and apply it to obtain a (δ V)d / 2 bound for perturbations of suitable periodic Schrödinger operators and a (not quite) Lieb-Thirring bound for perturbations of algebro-geometric almost periodic Jacobi matrices. © 2007 Elsevier Inc. All rights reserved.
Hundertmark, D., & Simon, B. (2008). Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices. Journal of Mathematical Analysis and Applications, 340(2), 892–900. https://doi.org/10.1016/j.jmaa.2007.08.059