Supercyclic vectors and the Angle Criterion

Eva A. Gallardo-Gutiérrez ¹   ; Jonathan R. Partington ²

¹ Departamento de Matemáticas Universidad de Zaragoza Plaza San Francisco s/n 50009 Zaragoza, Spain
² School of Mathematics University of Leeds Leeds LS2 9JT, U.K.

Studia Mathematica, Tome 166 (2005) no. 1, pp. 93-99

Résumé

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.

Détail

DOI : 10.4064/sm166-1-7

Keywords: angle criterion testing supercyclic vectors depends essential geometrical properties underlying space particular exhibit non supercyclic vectors backward shift acting still satisfy criterion nevertheless mathcal locally uniformly convex banach space angle criterion yields equivalent condition vector supercyclic furthermore prove local uniform convexity cannot weakened strict convexity