Perturbation of orthonormal bases with an application to diagonalization.
type: Item
instance of: scholarly article
title: Perturbation of orthonormal bases with an application to diagonalization.
zbMATH Open document ID: 1043.47019
DOI: 10.1007/BF01193675
author: H. Bercovici
author: Stoyko Kostov
published in: Integral Equations and Operator Theory
publication date: 2002-01-01T00:00:00Z
review text: Given an orthonormal basis \(\{e_n\}_{n=1}^\infty\) in a Hilbert space \(H\) and a dense linear manifold \(D\subset H\), the authors show that there exists a unitary operator \(V\) on \(H\) such that \(I-V\) is a trace class operator with arbitrarily small trace norm, and \(Ve_j\in D\) for all \(j\). This result can be used to simplify certain arguments of \textit{J.-B. Xia} [J. Funct. Anal. 145, 491--526 (1997; Zbl 0880.47027)] concerning the simultaneous diagonalization of operators on a space of square integrable functions.
reviewed by: Aleksej Turnšek
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 46C07
zbMATH DE Number: 1890566
zbMATH Keywords: orthonormal base
zbMATH Keywords: unitary operator
zbMATH Keywords: trace class
MaRDI profile type: Publication
cites work: Q5571194
cites work: Q3891239
cites work: Diagonalization modulo norm ideals with Lipschitz estimates
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description: scientific article; zbMATH DE number 1890566