Hypercyclic subsets

Abstract : We completely characterize the finite dimensional subsets A of any separable Hilbert space for which the notion of A-hypercyclicity coincides with the notion of hypercyclicity, where an operator T on a topological vector space X is said to be A-hypercyclic if the set {T n x, n ≥ 0, x ∈ A} is dense in X. We give a partial description for non necessarily finite dimensional subsets. We also characterize the finite dimensional subsets A of any separable Hilbert space H for which the somewhere density in H of {T n x, n ≥ 0, x ∈ A} implies the hypercyclicity of T. We provide a partial description for infinite dimensional subsets. These improve results of Costakis and Peris, Bourdon and Feldman, and Charpentier, Ernst and Menet, and answer a number of related open questions.
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Submitted on : Tuesday, August 14, 2018 - 5:22:50 PM
Last modification on : Monday, March 4, 2019 - 2:04:22 PM

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  • HAL Id : hal-01651264, version 4
  • ARXIV : 1711.10932

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S. Charpentier, R. Ernst. Hypercyclic subsets. 2018. ⟨hal-01651264v4⟩

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