, Volume 50, Issue 3, pp 385-391

Rotations of Hypercyclic and Supercyclic Operators

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Abstract.

Let T  ∈  B(X) be a hypercyclic operator and λ a complex number of modulus 1. Then λ T is hypercyclic and has the same set of hypercyclic vectors as T. A version of this results gives for a wide class of supercyclic operators that x ∈ X is supercyclic for T if and only if the set {tT n x  :  t > 0, n = 0, 1, ...} is dense in X. This gives answers to several questions studied in the literature.