Lieb-Thirring type inequalities for non-self-adjoint perturbations of magnetic Schrodinger operators

Let H := Ho + V and Hi := H-0,H-perpendicular to + V be respectively perturbations of the unperturbed Schrodinger operators Ho on L-2 (R-3) and H-0,H-perpendicular to on L2 (R-2) with constant magnetic field of strength b > 0, and V a complex relatively compact perturbation. We prove Lieb-Thirring type inequalities on the discrete spectrum of H and Hi. In particular, these estimates give a priori information on the distribution of eigenvalues around the Landau levels of the operator, and describe how fast sequences of eigenvalues converge. (C) 2014 Elsevier Inc. All rights reserved.