Hypercyclic operators with an infinite dimensional closed subspace of periodic points.
type: Item
instance of: scholarly article
title: Hypercyclic operators with an infinite dimensional closed subspace of periodic points.
zbMATH Open document ID: 1062.47012
author: Sophie Grivaux
published in: Revista Matemática Complutense
publication date: 2004-06-22T00:00:00Z
full work available at URL: https://eudml.org/doc/44503
review text: Let \(X\) be an infinite-dimensional real or complex separable Banach space \(X\). If \(T\) is a bounded operator on \(X\), a vector \(x\) of \(X\) is said to be hypercyclic for \(T\) if the orbit of \(x\) under \(T\), that is, the set \(\{T^{n}x: n \geq 0 \}\), is dense in \(X\). If \(T\) has a hypercyclic vector, \(T\) is called a hypercyclic operator. In the paper under review, the author proves that if \(X\) is an infinite-dimensional separable Banach space, then there exists a hypercyclic operator on \(X\) which is equal to the identity operator on an infinite-dimensional closed subspace of \(X\).
reviewed by: Ömer Gök
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 2076534
zbMATH Keywords: separable Banach spaces
zbMATH Keywords: hypercyclic vectors
zbMATH Keywords: hypercyclic operators
zbMATH Keywords: chaotic operators
MaRDI profile type: Publication
DOI: 10.5209/REV_REMA.2003.V16.N2.16809
description: scientific article; zbMATH DE number 2076534