A hypercyclic rank one perturbation of a unitary operator
type: Item
instance of: scholarly article
title: A hypercyclic rank one perturbation of a unitary operator
zbMATH Open document ID: 1251.47007
author: Sophie Grivaux
published in: Mathematische Nachrichten
publication date: 2012-05-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1010.3598
Mathematics Subject Classification ID: 47A16
zbMATH DE Number: 6034374
zbMATH Keywords: linear dynamical systems
zbMATH Keywords: hypercyclic operators
zbMATH Keywords: finite rank perturbations
zbMATH Keywords: unitary operators
MaRDI profile type: Publication
OpenAlex ID: W2128763848
arXiv ID: 1010.3598
cites work: Existence of hypercyclic operators on topological vector spaces
cites work: Hypercyclicity and unimodular point spectrum
cites work: Frequently hypercyclic operators
cites work: Q3638111
cites work: A PROBLEM OF SALEM AND ZYGMUND ON THE SMOOTHNESS OF AN ANALYTIC FUNCTION THAT GENERATES A PEANO CURVE
cites work: On hypercyclic operators on Banach spaces
cites work: Orbits of hyponormal operators
cites work: A new class of frequently hypercyclic operators
cites work: Q5182704
cites work: On orbits of elements
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cites work: Supercyclicity and weighted shifts
cites work: A hypercyclic finite rank perturbation of a unitary operator
DOI: 10.1002/MANA.201000112
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review text: In this paper, the author is interested in the construction of some special hypercyclic operators on Hilbert spaces and proves that there exists a rank \(1\) perturbation of a unitary operator on a complex separable infinite-dimensional Hilbert space which is hypercyclic.
reviewed by: Ömer Gök
description: scientific article; zbMATH DE number 6034374