We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ℬ. Our result extends a recent result on hypercyclicity on the operator algebra of a Hilbert space. This kind of result is a powerful tool to analyze the structure of supercyclic vectors of a supercyclic operator that is defined on ℬ. For instance, as a consequence of the main result, we give a very simple proof of the recently established fact that certain supercyclic operators defined on a Banach space have an infinite-dimensional closed subspace of supercyclic vectors.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-3-1,
author = {Alfonso Montes-Rodr\'\i guez and M. Carmen Romero-Moreno},
title = {Supercyclicity in the operator algebra},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {201-213},
zbl = {1006.47009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-3-1}
}
Alfonso Montes-Rodríguez; M. Carmen Romero-Moreno. Supercyclicity in the operator algebra. Studia Mathematica, Tome 151 (2002) pp. 201-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-3-1/