Lieb-Thirring estimates for non-selfadjoint Schrödinger 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
Published: 2008
Subjects:
laptev
Online Access:http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.311.2528
http://arxiv.org/pdf/0806.1393v1.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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