Asymptotic intertwining by the identity operator and permanence of spectral properties
type: Item
instance of: scholarly article
title: Asymptotic intertwining by the identity operator and permanence of spectral properties
zbMATH Open document ID: 1287.47003
published in: Banach Journal of Mathematical Analysis
publication date: 2013-03-20T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bjma/1358864558
review text: Let \(A, B\in B(X)\), \(X\) a Banach space. \(B\) is said to be asymptotically intertwined to \(A\) by the identity operator \(I\in B(X)\) if \(\lim_{n\to\infty}\|\Delta^{n}_{AB}(I)\|^{\frac{1}{n}}=0\), where \(\Delta_{AB}(I)=AI-IB=A-B\). The paper studies certain spectral properties preserved by the above relation. Some interesting results are obtained when \(\Delta_{AB}(I)\) is nilpotent and, more generally, for \(B\) asymptotically intertwined to \(A\) by the identity, but when \(\Delta_{AB}(I)\) is not nilpotent.
reviewed by: C. Carpintero
Mathematics Subject Classification ID: 47A11
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 6147129
zbMATH Keywords: asymptotically intertwined
zbMATH Keywords: SVEP
zbMATH Keywords: polaroid operator
zbMATH Keywords: spectral properties
zbMATH Keywords: property \((\delta)\)
author: B. P. Duggal
MaRDI profile type: Publication
OpenAlex ID: W2058625824
DOI: 10.15352/BJMA/1358864558
description: scientific article; zbMATH DE number 6147129