Non-symmetric perturbations of self-adjoint operators

Cuenin, Jean-Claude; Tretter, Christiane (2016). Non-symmetric perturbations of self-adjoint operators. Journal of mathematical analysis and applications, 441(1), pp. 235-258. Elsevier 10.1016/j.jmaa.2016.03.070

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Cuenin, Jean-Claude and Tretter, Christiane

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-247X

Publisher:

Elsevier

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

07 Aug 2017 16:45

Last Modified:

02 Sep 2018 02:30

Publisher DOI:

10.1016/j.jmaa.2016.03.070

BORIS DOI:

10.7892/boris.99766

URI:

https://boris.unibe.ch/id/eprint/99766

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