Dual disjoint hypercyclic operators

Let E be a separable Fréchet space. The operators T 1 , … , T m are disjoint hypercyclic if there exists x ∈ E such that the orbit of ( x , … , x ) under ( T 1 , … , T m ) is dense in E × ⋯ × E . We show that every separable Banach space E admits an m-tuple of bounded linear operators which are disj...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 374; no. 1; pp. 106 - 117
Main Author:	Salas, Héctor N.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Inc 01-02-2011 Elsevier
Subjects:	Disjoint hypercyclic operators Dual hypercyclic operators Exact sciences and technology Functional analysis Hypercyclic vectors Mathematical analysis Mathematics Operator theory Sciences and techniques of general use Disjoint hypercyclic operators Hypercyclic vectors Dual hypercyclic operators Hypercyclic vector Mathematical analysis Bounded operator Banach space Linear operator
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Summary:	Let E be a separable Fréchet space. The operators T 1 , … , T m are disjoint hypercyclic if there exists x ∈ E such that the orbit of ( x , … , x ) under ( T 1 , … , T m ) is dense in E × ⋯ × E . We show that every separable Banach space E admits an m-tuple of bounded linear operators which are disjoint hypercyclic. If, in addition, its dual E ∗ is separable, then they can be constructed such that T 1 ∗ , … , T m ∗ are also disjoint hypercyclic.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2010.09.003