Supercyclicity in the operator algebra
Volume 150 / 2002
Studia Mathematica 150 (2002), 201-213
MSC: Primary 47A16.
DOI: 10.4064/sm150-3-1
Abstract
We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ${\cal B}$. 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 ${\cal B}$. 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.
