On products of hypercyclic semigroups
type: Item
instance of: scholarly article
title: On products of hypercyclic semigroups
zbMATH Open document ID: 1103.47027
author: W. Desch
author: W. Schappacher
published in: Semigroup Forum
publication date: 2006-03-22T00:00:00Z
review text: If \(X\) is a separable infinite-dimensional Banach space and \(J=\mathbb{N}\) or \(\mathbb{R}_{+}\), a semigroup \((S(t))_{t\in J}\) with values in \(X\) is hypercyclic if there exists a vector \(x\in X\) such that the orbit \(\{S(t)x ; t\in J\}\) is dense in \(X\). If such a semigroup is hypercyclic, it is known that \((S(t)\times S(t))_{t\in J}\) is hypercyclic on \(X\times X\) if and only if it satisfies the so-called Hypercyclicity Criterion. The authors give a condition, which they call the Recurrent Hypercyclicity Criterion, which is necessary and sufficient for \((S(t))_{t\in J}\) to have the property that \((S(t)\times T(t))_{t\in J}\) is hypercyclic for every semigroup \((T(t))_{t\in J}\) satisfying the Hypercyclicity Criterion.
reviewed by: Sophie Grivaux
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47A16
zbMATH DE Number: 5014186
zbMATH Keywords: hypercyclic semigroups chaotic
zbMATH Keywords: hypercyclicity criterion
MaRDI profile type: Publication
full work available at URL: s00233-005-0523-z
OpenAlex ID: W2034565201
DOI: 10.1007/S00233-005-0523-Z
description: scientific article; zbMATH DE number 5014186