On existence of hyperinvariant subspaces for linear maps
type: Item
instance of: scholarly article
title: On existence of hyperinvariant subspaces for linear maps
zbMATH Open document ID: 1171.47004
published in: Banach Journal of Mathematical Analysis
publication date: 2008-12-09T00:00:00Z
full work available at URL: https://eudml.org/doc/55930
full work available at URL: v3n1.htm
review text: Let \(X\) be an infinite-dimensional complex vector space and let \(T\in L(X)\) be non-constant. In this paper, it is proved that \(T\) has a proper hyperinvariant subspace iff \(\sigma(T)\neq\emptyset\). As an application, it is shown that \(T'\) is transitive iff either \(T=\alpha I\) for some \(\alpha\in\mathbb C\), or \(\sigma(T)=\emptyset\). Also, it is proved that if \(X\) is the complex space of all sequences, then \(T\) has a proper closed hyperinvariant subspace.
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 5379957
zbMATH Keywords: hyperinvariant subspace
zbMATH Keywords: locally convex space
zbMATH Keywords: endomorphism
author: Wiesław Tadeusz Żelazko
reviewed by: Bahmann Yousefi
MaRDI profile type: Publication
OpenAlex ID: W2074516890
DOI: 10.15352/BJMA/1240336431
description: scientific article; zbMATH DE number 5379957