Supercyclic vectors and the Angle Criterion

Eva A. Gallardo-Gutiérrez, and Jonathan R. Partington. "Supercyclic vectors and the Angle Criterion." Studia Mathematica 166.1 (2005): 93-99. <http://eudml.org/doc/285168>.

@article{EvaA2005,
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 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.},
author = {Eva A. Gallardo-Gutiérrez, Jonathan R. Partington},
journal = {Studia Mathematica},
keywords = {supercyclic operators; supercyclic vectors; Angle Criterion},
language = {eng},
number = {1},
pages = {93-99},
title = {Supercyclic vectors and the Angle Criterion},
url = {http://eudml.org/doc/285168},
volume = {166},
year = {2005},
}

TY - JOUR
AU - Eva A. Gallardo-Gutiérrez
AU - Jonathan R. Partington
TI - Supercyclic vectors and the Angle Criterion
JO - Studia Mathematica
PY - 2005
VL - 166
IS - 1
SP - 93
EP - 99
AB - 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.
LA - eng
KW - supercyclic operators; supercyclic vectors; Angle Criterion
UR - http://eudml.org/doc/285168
ER -