Supercyclic vectors and the Angle Criterion
Volume 166 / 2005
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.
