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Disjoint hypercyclicity, Sidon sets and weakly mixing operators

Part of: Sequences and sets Topological dynamics General theory of linear operators

Published online by Cambridge University Press:  22 August 2023

RODRIGO CARDECCIA Open the ORCID record for RODRIGO CARDECCIA [Opens in a new window]
RODRIGO CARDECCIA*
Affiliation:
Instituto Balseiro, Universidad Nacional de Cuyo – C.N.E.A. and CONICET, Av. Bustillo 9500, San Carlos de Bariloche, R8402AGP, Argentina
*
e-mail: rodrigo.cardeccia@ib.edu.ar
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Abstract

We prove that a finite set of natural numbers J satisfies that $J\cup \{0\}$ is not Sidon if and only if for any operator T, the disjoint hypercyclicity of $\{T^j:j\in J\}$ implies that T is weakly mixing. As an application we show the existence of a non-weakly mixing operator T such that $T\oplus T^2\oplus\cdots \oplus T^n$ is hypercyclic for every n.

Keywords

Sidon setsdisjoint hypercyclicitynon-weakly mixing operators

MSC classification

Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 37B99: None of the above, but in this section
Secondary: 11B99: None of the above, but in this section
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 5 , May 2024 , pp. 1315 - 1329
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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