Lieb-Thirring estimates for non self-adjoint Schrödinger operators
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 estimat...
Published in: | Journal of Mathematical Physics |
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Main Authors: | , |
Format: | Other/Unknown Material |
Language: | English |
Published: |
American Institute of Physics (AIP)
2008
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Subjects: | |
Online Access: | https://oskar-bordeaux.fr/handle/20.500.12278/116612 https://doi.org/10.1063/1.2969028 |
Summary: | 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. |
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