The invariant subspace problem for a class of Banach spaces, 2: Hypercyclic operators

  title={The invariant subspace problem for a class of Banach spaces, 2: Hypercyclic operators},
  author={Charles John Read},
  journal={Israel Journal of Mathematics},
  • C. J. Read
  • Published 1988
  • Mathematics
  • Israel Journal of Mathematics
We continue here the line of investigation begun in [7], where we showed that on every Banach spaceX=l1⊗W (whereW is separable) there is an operatorT with no nontrivial invariant subspaces. Here, we work on the same class of Banach spaces, and produce operators which not only have no invariant subspaces, but are also hypercyclic. This means that for every nonzero vectorx inX, the translatesTr x (r=1, 2, 3,...) are dense inX. This is an interesting result even if stated in a form which… Expand
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