Coexistence of spectra in rank-one perturbation problems.
type: Item
instance of: scholarly article
title: Coexistence of spectra in rank-one perturbation problems.
zbMATH Open document ID: 1059.47020
author: S. Fuentes
author: Rafael del Rio
author: Alexei Poltoratski
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2004-03-11T00:00:00Z
review text: Let \(A_0\) be a selfadjoint operator in a separable Hilbert space. Let \(A_\lambda= A_0+\lambda(.,\varphi)\varphi\), \(\lambda\in\mathbb{R}\). The following result is proven: For any measurable set \(B\subset\mathbb{R}\) there exists a family of rank one perturbations \(\{A_\lambda\}\) such that \(A_\lambda\) has dense absolutely continuous and dense singular spectrum for almost every \(\lambda\in B\) and dense absolutely continuous (but no singular) spectrum for almost every \(\lambda\not\in B\).
reviewed by: Michael Demuth
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 81Q15
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 1809797
zbMATH Keywords: family of rank one perturbations
zbMATH Keywords: dense spectrum
zbMATH Keywords: absolutely continuous spectrum
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1809797