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Disjoint hypercyclicity, Sidon sets and weakly mixing operators
Published online by Cambridge University Press: 22 August 2023
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.
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- © The Author(s), 2023. Published by Cambridge University Press