A note on J-sets of linear operators

Original Paper


We construct a Banach space operator \({T \in B(X)}\) such that the set J T (0) has a nonempty interior but J T (0) ≠ X. This gives a negative answer to a problem raised by Costakis and Manoussos (J. Oper. Theory [in press], 2011).


Hypercyclic vectors Orbits J-sets 

Mathematics Subject Classification (2000)



  1. 1.
    Bourdon P.S., Feldman N.S.: Somewhere dense orbits are everywhere dense. Indiana Univ. Math. J. 52, 811–819 (2003)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Costakis, G., Manoussos, A.: J-class operators and hypercyclicity. J. Oper. Theory (to appear) (2011)Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Faculty of Mathematical SciencesUniversity of TabrizTabrizIran
  2. 2.Mathematical InstituteCzech Academy of SciencesPraha 1Czech Republic

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