Lieb-Thirring estimates for non self-adjoint Schrödinger operators

• Published in: Journal of Mathematical Physics
• Main Authors: Bruneau, Vincent, Ouhabaz, E.-M.
• Other Authors: Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2008
• Subjects: [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]; [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]; laptev
• Online Access: https://hal.archives-ouvertes.fr/hal-00286274; https://hal.archives-ouvertes.fr/hal-00286274/document; https://hal.archives-ouvertes.fr/hal-00286274/file/Lieb-ThirringNSA7.pdf; https://doi.org/10.1063/1.2969028

International audience 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.