On the spectrum and numerical range of tridiagonal random operators

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dc.identifier.uri http://dx.doi.org/10.15488/2340
dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/2366
dc.contributor.author Hagger, Raffael
dc.date.accessioned 2017-11-17T10:07:36Z
dc.date.available 2017-11-17T10:07:36Z
dc.date.issued 2016
dc.identifier.citation Hagger, R.: On the spectrum and numerical range of tridiagonal random operators. In: Journal of Spectral Theory 6 (2016), Nr. 2, S. 215-266. DOI: https://doi.org/10.4171/JST/124
dc.description.abstract In this paper we derive an explicit formula for the numerical range of (non-selfadjoint) tridiagonal random operators. As a corollary we obtain that the numerical range of such an operator is always the convex hull of its spectrum, this (surprisingly) holding whether or not the random operator is normal. Furthermore, we introduce a method to compute numerical ranges of (not necessarily random) tridiagonal operators that is based on the Schur test. In a somewhat combinatorial approachwe use thismethod to compute the numerical range of the square of the (generalized) Feinberg-Zee random hopping matrix to obtain an improved upper bound to the spectrum. In particular, we show that the spectrum of the Feinberg-Zee random hopping matrix is not convex. © European Mathematical Society. eng
dc.language.iso eng
dc.publisher Zürich : European Mathematical Society Publishing House
dc.relation.ispartofseries Journal of Spectral Theory 6 (2016), Nr. 2
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
dc.subject Numerical range eng
dc.subject Pseudo-ergodic eng
dc.subject Random operator eng
dc.subject Spectrum eng
dc.subject Tridiagonal eng
dc.subject.ddc 530 | Physik ger
dc.title On the spectrum and numerical range of tridiagonal random operators
dc.type article
dc.type Text
dc.relation.issn 1664-039X
dc.relation.doi https://doi.org/10.4171/JST/124
dc.bibliographicCitation.issue 2
dc.bibliographicCitation.volume 6
dc.bibliographicCitation.firstPage 215
dc.bibliographicCitation.lastPage 266
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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