Ouhabaz: Lieb-Thirring estimates for non-self-adjoint Schr ¨ dinger operators

Abstract. For general non-symmetric operators A, we prove that the moment of order γ ≥ 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-ad...

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Bibliographic Details
Main Authors: Vincent Bruneau, El, Maati Ouhabaz
Other Authors: The Pennsylvania State University CiteSeerX Archives
Format: Text
Language:English
Subjects:
k=1
laptev
Online Access:http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.433.7343
http://www.math.u-bordeaux.fr/~vbruneau/BruOuh.pdf
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Summary:Abstract. For general non-symmetric operators A, we prove that the moment of order γ ≥ 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 [11]. We also discuss moment of resonances of Schrödinger self-adjoint operators. 1.

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