Operators similar to their restrictions to invariant subspaces
type: Item
instance of: scholarly article
title: Operators similar to their restrictions to invariant subspaces
zbMATH Open document ID: 1329.47015
author: Xinjun Xu
author: You Qing Ji
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-01-26T00:00:00Z
review text: Let \(X\) be a separable infinite-dimensional Banach space and \(T\in B(X)\). The operator \(T\) is called crystal-like if, for each nonzero invariant subspace \(M\) of \(T\), there exists a positive number \(r\) such the restriction of \(T\) to \(M\) is similar to \(rT\). In this paper, the authors study several elementary properties of this new interesting operator class, including the spectrum, cyclicity, strong irreducibility, essential similarity, reflectivity and the commutativity of the commutant. A plethora of examples are provided and some open problems are also given.
reviewed by: Kui Ji
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 47A46
zbMATH DE Number: 6390681
zbMATH Keywords: crystal-like operator
zbMATH Keywords: spectrum
zbMATH Keywords: irreducibility
zbMATH Keywords: reflexivity
MaRDI profile type: Publication
full work available at URL: j.jmaa.2014.02.017
OpenAlex ID: W1980178252
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DOI: 10.1016/J.JMAA.2014.02.017
description: scientific article; zbMATH DE number 6390681