On weak positive supercyclicity
type: Item
instance of: scholarly article
title: On weak positive supercyclicity
zbMATH Open document ID: 1162.47009
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: Let \(X\) be a complex topological vector space and let \({\mathcal M}'\) be the commutant of a semigroup \({\mathcal M}\) of continuous linear operators on \(X\). The main result of this paper states that if there is an operator \(T\in{\mathcal M}\cap{\mathcal M}'\) which is not a multiple of the identity and for which \(p(T)\) has dense range for all polynomials \(p\) such that \(p(T)\not=0\), and if for some \(x\in X\), the set \(\{\lambda Sx:|\lambda|=1\text{ and }S\in{\mathcal M}\}\) is dense in \(X\), then the set \(\{Sx:S\in{\mathcal M}\}\) is dense in \(X\). From this result, the authors derive several consequences regarding hypercyclic, weakly hypercyclic, supercyclic and weakly supercyclic operators.
reviewed by: Abdellatif Bourhim
Mathematics Subject Classification ID: 47A16
zbMATH DE Number: 5508710
zbMATH Keywords: hypercyclicity
zbMATH Keywords: supercyclicity
zbMATH Keywords: weak hypercyclicity
zbMATH Keywords: weak supercyclicity
author: Fernando León-Saavedra
author: Antonio Piqueras-Lerena
MaRDI profile type: Publication
full work available at URL: s11856-008-1050-x
OpenAlex ID: W2023697908
cites work: Q4243021
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cites work: Invariant subspaces and the exponential map
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cites work: n-supercyclic operators
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cites work: LIMITS OF WEAKLY HYPERCYCLIC AND SUPERCYCLIC OPERATORS
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DOI: 10.1007/S11856-008-1050-X
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description: scientific article; zbMATH DE number 5508710