Integral Equations and Operator Theory

, Volume 50, Issue 3, pp 385–391

Rotations of Hypercyclic and Supercyclic Operators

Original Paper

DOI: 10.1007/s00020-003-1299-8

Cite this article as:
León-Saavedra, F. & Müller, V. Integr. equ. oper. theory (2004) 50: 385. doi:10.1007/s00020-003-1299-8

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 {tTnx  :  t > 0, n = 0, 1, ...} is dense in X. This gives answers to several questions studied in the literature.

Mathematics Subject Classification (2000).

47A16 

Keywords.

Hypercyclic vectors supercyclic vectors 

Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Dpto. de Matemáticas, Facultad de CienciasUniversidad de CádizPuerto RealSpain
  2. 2.Mathematical InstituteCzech Academy of SciencesPrague 1Czech Republic

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