Lieb-Thirring estimates for non self-adjoint Schrödinger operators

Vincent Bruneau; E. -M. Ouhabaz

doi:10.1063/1.2969028

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arXiv · 0806.1393

Lieb-Thirring estimates for non self-adjoint Schrödinger operators

Vincent Bruneau·E. -M. Ouhabaz

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Abstract

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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BibTeX RIS

Vincent Bruneau, E. -M. Ouhabaz. 2008-06-09. Lieb-Thirring estimates for non self-adjoint Schrödinger operators. https://doi.org/10.1063/1.2969028

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