Lieb-Thirring estimates for non self-adjoint Schrödinger operators

Bruneau, Vincent; Ouhabaz, E. -M.

Lieb-Thirring estimates for non self-adjoint Schrödinger operators

Authors

Description

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.