English

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

Functional Analysis 2021-06-03 v2

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 TT such that TTT \oplus T is frequently hypercyclic, the set of operators SS such that T,ST, S are disjoint frequently hypercyclic but fail to satisfy the Disjoint Hypercyclicity Criterion is SOT dense in the algebra of bounded linear operators.

Keywords

Cite

@article{arxiv.2102.11961,
  title  = {Existence of disjoint frequently hypercyclic operators which fail to be disjoint weakly mixing},
  author = {Özgür Martin and Yunied Puig},
  journal= {arXiv preprint arXiv:2102.11961},
  year   = {2021}
}