Existence of disjoint frequently hypercyclic operators which fail to be disjoint weakly mixing

Özgür Martin; Yunied Puig

doi:10.1016/j.jmaa.2021.125106

Existence of disjoint frequently hypercyclic operators which fail to be disjoint weakly mixing

Özgür Martin, Yunied Puig

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this short note, we answer a question of Martin and Sanders [Integr. Equ. Oper. Theory, 85 (2) (2016), 191-220] by showing the existence of disjoint frequently hypercyclic operators which fail to be disjoint weakly mixing and, therefore, fail to satisfy the Disjoint Hypercyclicity Criterion. We also show that given an operator T such that T⊕T is frequently hypercyclic, the set of operators S such that T,S are disjoint frequently hypercyclic but fail to satisfy the Disjoint Hypercyclicity Criterion is SOT dense in the algebra of bounded linear operators.

Original language	English
Article number	125106
Journal	Journal of Mathematical Analysis and Applications
Volume	500
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2021.125106
State	Published - 1 Aug 2021
Externally published	Yes

Keywords

Disjoint frequent hypercyclicity
Disjoint hypercyclicity
Frequently hypercyclic operator
Hypercyclic operator

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2021.125106

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AB - In this short note, we answer a question of Martin and Sanders [Integr. Equ. Oper. Theory, 85 (2) (2016), 191-220] by showing the existence of disjoint frequently hypercyclic operators which fail to be disjoint weakly mixing and, therefore, fail to satisfy the Disjoint Hypercyclicity Criterion. We also show that given an operator T such that T⊕T is frequently hypercyclic, the set of operators S such that T,S are disjoint frequently hypercyclic but fail to satisfy the Disjoint Hypercyclicity Criterion is SOT dense in the algebra of bounded linear operators.

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KW - Frequently hypercyclic operator

KW - Hypercyclic operator

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Existence of disjoint frequently hypercyclic operators which fail to be disjoint weakly mixing

Abstract

Keywords

ASJC Scopus subject areas

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