Hypercyclic operators are subspace hypercyclic
type: Item
instance of: scholarly article
title: Hypercyclic operators are subspace hypercyclic
zbMATH Open document ID: 1342.47009
author: Nareen Bamerni
author: Adem Kilicman
author: Vladimir Kadets
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-12-21T00:00:00Z
review text: A bounded operator \(T\) on a separable Banach space \(X\) is called subspace hypercyclic for a subspace \(M\) of \(X\) if there is a vector \(x \in X\) such that the intersection of its orbit and \(M\) is dense in \(M\). The aim of this paper is to solve a question of \textit{B. F. Madore} and \textit{R. A. Martínez-Avendaño} [J. Math. Anal. Appl. 373, No. 2, 502--511 (2011; Zbl 1210.47023)] and prove that if \(T\) is a hypercyclic operator on \(X\), then there is a non-trivial closed subspace \(M\) of \(X\) such that \(T\) is hypercyclic for \(M\). To do this, they show that, if \(A\) is a dense subset of a Banach space \(X\), then there is a non-trivial closed subspace \(M\) such that \(A \cap M\) is dense in \(M\).
Mathematics Subject Classification ID: 47A16
zbMATH DE Number: 6522745
zbMATH Keywords: hypercyclicity
zbMATH Keywords: subspace-hypercyclicity
reviewed by: José Bonet
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.11.015
OpenAlex ID: W2137495889
cites work: Hypercyclic and cyclic vectors
cites work: Existence of hypercyclic operators on topological vector spaces
cites work: Q5182704
cites work: Some questions about subspace-hypercyclic operators
cites work: On subspace-hypercyclic operators
cites work: Rotations of hypercyclic and supercyclic operators
cites work: Subspace hypercyclicity
cites work: Subspace hypercyclicity for Toeplitz operators
cites work: Notes on subspace-hypercyclic operators
cites work: On orbits of elements
DOI: 10.1016/J.JMAA.2015.11.015
description: scientific article; zbMATH DE number 6522745