Tuple of operators and hypercyclicity criterion
type: Item
instance of: scholarly article
zbMATH Open document ID: 1268.47010
author: Bahmann Yousefi
author: G. H. R. Moghimi
publication date: 2012-09-14T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47B33
zbMATH DE Number: 6082512
zbMATH Keywords: hypercyclic operator tuple
zbMATH Keywords: hypercyclic vector
zbMATH Keywords: hypercylicity criterion
zbMATH Keywords: hereditarily hypercyclicity
MaRDI profile type: Publication
title: Tuple of operators and hypercyclicity criterion
published in: International Journal of Pure and Applied Mathematics
review text: If \(X\) is a separable Banach space and \((T_{m})_{m\geq 0}\) is a sequence of bounded linear operators on \(X\), the sequence \((T_{m})_{m\geq 0}\) is said to be hypercyclic if there exists a vector \(x\in X\) such that the set \(\{T_{m}x : m\geq 0\}\) is dense in \(X\). When \(T\) is a bounded operator and \(T_{m}=T^{m}\) for each \(m\), then \(T\) itself is said to be hypercyclic. In the present paper as well as in the companion paper [ibid. 76, No.~3, 349--354 (2012; Zbl 1268.47011)], the authors study the case where the sequence \((T_{m})_{m\geq 0}\) is given by all powers \(T_{1}^{k_{1}}T_{2}^{k_{2}}\dots T_{n}^{k_{n}}\), where \(T_{1},\dots, T_{n}\) are \(n\) commuting operators on \(X\), and give versions in this setting of well-known criteria for hypercyclicity.
reviewed by: Sophie Grivaux
description: scientific article; zbMATH DE number 6082512