Lieb-Thirring estimates for non self-adjoint Schrödinger operators
For general non-symmetric operators $A$, we prove that the moment of order $γ\ge 1$ of negative real-parts of its eigenvalues is bounded by the moment of order $γ$ of negative eigenvalues of its symmetric part $H = {1/2} [A + A^*].$ As an application, we obtain Lieb-Thirring estimates for non self-a...
| Main Authors: | , |
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| Format: | Text |
| Language: | unknown |
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arXiv
2008
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| Online Access: | https://dx.doi.org/10.48550/arxiv.0806.1393 https://arxiv.org/abs/0806.1393 |
| Summary: | For general non-symmetric operators $A$, we prove that the moment of order $γ\ge 1$ of negative real-parts of its eigenvalues is bounded by the moment of order $γ$ of negative eigenvalues of its symmetric part $H = {1/2} [A + A^*].$ 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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