Publication: Supercyclic vectors and the Angle Criterion
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2005
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Polish Acad Sciencies Inst Mathematics
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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.