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Disjoint hypercyclicity, Sidon sets and weakly mixing operators

Published online by Cambridge University Press:  22 August 2023

Instituto Balseiro, Universidad Nacional de Cuyo – C.N.E.A. and CONICET, Av. Bustillo 9500, San Carlos de Bariloche, R8402AGP, Argentina


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.

Original Article
© The Author(s), 2023. Published by Cambridge University Press

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