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Gallardo Gutiérrez, Eva A. and Partington, Jonathan R.
(2005)
*Supercyclic vectors and the Angle Criterion.*
Studia Mathematica, 166
(1).
pp. 93-99.
ISSN 0039-3223

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## 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 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.

Item Type: | Article |
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Uncontrolled Keywords: | supercyclic operators; supercyclic vectors; Angle Criterion |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 21105 |

Deposited On: | 26 Apr 2013 08:45 |

Last Modified: | 07 Feb 2014 10:25 |

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