Lieb-Thirring estimates for non self-adjoint Schrödinger operators

Vincent Bruneau (1) , E.-M. Ouhabaz (1)

1 IMB - Institut de Mathématiques de Bordeaux

For general non-symmetric operators $A$, we prove that the moment of order $\gamma \ge 1$ of negative real-parts of its eigenvalues is bounded by the moment of order $\gamma$ of negative eigenvalues of its symmetric part $H = \frac{1}{2} [A + A^*].$ As an application, we obtain Lieb-Thirring estimates for non self-adjoint Schrödinger operators. In particular, we recover recent results by Frank, Laptev, Lieb and Seiringer \cite{FLLS}. We also discuss moment of resonances of Schrödinger self-adjoint operators.

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]

Vincent Bruneau, E.-M. Ouhabaz. Lieb-Thirring estimates for non self-adjoint Schrödinger operators. Journal of Mathematical Physics, 2008, 49, pp.093504. ⟨10.1063/1.2969028⟩. ⟨hal-00286274⟩