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Rotations of Hypercyclic and Supercyclic Operators |
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| Authors: | |
| Institution: | (1) Dpto. de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, Pol. Rio San Pedro S/N, 11500 Puerto Real, Spain;(2) Mathematical Institute, Czech Academy of Sciences, Zitná 25, 115 67 Prague 1, Czech Republic |
| Abstract: | Let T  B(X) be a hypercyclic operator and  a complex number of modulus 1. Then 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 {tTn x : t > 0, n = 0, 1, ...} is dense in X. This gives answers to several questions studied in the literature. |
| Keywords: | 47A16 |
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