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

Let $H := H {0} + V$ and $H {\perp} := H {0,\perp} + V$ be respectively perturbations of the free Schr\-odinger operators $H {0}$ on $L^{2}\big\mathbb{R}^{2d+1}\big$ and $H {0,\perp}$ on $L^{2}\big\mathbb{R}^{2d}\big$, $d \geq 1$ with constant magnetic field of strength $b0$, and $V$ is a complex relatively compact perturbation. We prove Lieb-Thirring type inequalities for the discrete spectrum of $H$ and $H {\perp}$. In particular, these estimates give $a\, priori$ information on the distribution of the discrete eigenvalues around the Landau levels of the operator, and describe how fast sequences of eigenvalues converge.

Author: Diomba Sambou

Source: https://archive.org/