Non-symmetric perturbations of self-adjoint operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:441

Article

Cuenin, Jean-Claude¹  Tretter, Christiane² 

[1] Univ Munich, Math Inst, Theresienstr 39, D-80333 Munich, Germany

[2] Univ Bern, Math Inst, Sidlerstr 5, CH-3012 Bern, Switzerland

关键词: Spectrum;    Perturbation theory;    Non-selfadjoint operator;    Spectral gap;    Resolvent estimate;    Essential spectrum;   

DOI  :  10.1016/j.jmaa.2016.03.070

来源: Elsevier

【 摘 要 】

We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding resolvent estimates. These results extend, and improve, classical perturbation results by Kato and by Gohberg/Krein. Further, we study essential spectral gaps and perturbations exhibiting additional structure with respect to the unperturbed operator; in the latter case, we can even allow for perturbations with relative bound >= 1. The generality of our results is illustrated by several applications, massive and massless Dirac operators, point-coupled periodic systems, and two-channel Hamiltonians with dissipation. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free