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 c₀ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-7,
author = {Eva A. Gallardo-Guti\'errez and Jonathan R. Partington},
title = {Supercyclic vectors and the Angle Criterion},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {93-99},
zbl = {1073.47012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-7}
}
Eva A. Gallardo-Gutiérrez; Jonathan R. Partington. Supercyclic vectors and the Angle Criterion. Studia Mathematica, Tome 166 (2005) pp. 93-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-7/