Lieb-Thirring estimates for non self-adjoint Schrödinger operators

Details Lieb-Thirring estimates for non self-adjoint Schrödinger operators Lieb-Thirring estimates for non self-adjoint Schrödinger operators

2008-06-09

arxiv.org/abs/0806.1393v1

Journal of Mathematical Physics 49 (2008) 093504

Mathematics

Spectral Theory

Scientific paper

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 $H = {1/2} [A + A^*].$ As an application, we obtain Lieb-Thirring estimates for non self-adjoint Schr\"odinger operators. In particular, we recover recent results by Frank, Laptev, Lieb and Seiringer \cite{FLLS}. We also discuss moment of resonances of Schr\"odinger self-adjoint operators.

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