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Supercyclic vectors and the Angle Criterion

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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
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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