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Non-symmetric perturbations of self-adjoint operators

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journal contribution
posted on 02.12.2020, 09:34 by Jean-Claude CueninJean-Claude Cuenin, Christiane Tretter
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/Kreĭn. 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Mathematical Analysis and Applications

Volume

441

Issue

1

Pages

235 - 258

Publisher

Elsevier

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Journal of Mathematical Analysis and Applications and the definitive published version is available at https://doi.org/10.1016/j.jmaa.2016.03.070.

Acceptance date

12/01/2016

Publication date

2016-04-04

Copyright date

2016

ISSN

0022-247X

eISSN

1096-0813

Language

en

Depositor

Dr Jean-Claude Cuenin. Deposit date: 17 November 2020