Lieb-Thirring estimates for non self-adjoint Schrödinger operators

• Published in: Journal of Mathematical Physics
• Main Authors: BRUNEAU, Vincent, OUHABAZ, E.-M.
• Format: Other/Unknown Material
• Language: English
• Published: American Institute of Physics (AIP) 2008
• Subjects: Mathématiques [math]/Théorie spectrale [math.SP]; Mathématiques [math]/Physique mathématique [math-ph]; laptev
• Online Access: https://oskar-bordeaux.fr/handle/20.500.12278/116612; https://doi.org/10.1063/1.2969028

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.