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Supercyclic vectors and the Angle Criterion

Volume 166 / 2005

Eva A. Gallardo-Gutiérrez, Jonathan R. Partington Studia Mathematica 166 (2005), 93-99 MSC: Primary 47A16, 47A15. DOI: 10.4064/sm166-1-7

Abstract

We show that the Angle Criterion for testing supercyclic vectors depends in an essential way on the geometrical properties of the underlying space. In particular, we exhibit non-supercyclic vectors for the backward shift acting on $c_0$ that still satisfy such a criterion. Nevertheless, if ${\mathcal B}$ is a locally uniformly convex Banach space, the Angle Criterion yields an equivalent condition for a vector to be supercyclic. Furthermore, we prove that local uniform convexity cannot be weakened to strict convexity.

Authors

  • Eva A. Gallardo-GutiérrezDepartamento de Matemáticas
    Universidad de Zaragoza
    Plaza San Francisco s/n
    50009 Zaragoza, Spain
    e-mail
  • Jonathan R. PartingtonSchool of Mathematics
    University of Leeds
    Leeds LS2 9JT, U.K.
    e-mail

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