# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Supercyclicity in the operator algebra

### Tom 150 / 2002

Studia Mathematica 150 (2002), 201-213 MSC: Primary 47A16. DOI: 10.4064/sm150-3-1

#### Streszczenie

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.

#### Autorzy

• Alfonso Montes-RodríguezDepartamento de Análisis Matemático
Aptdo. 1160
41080 Sevilla, Spain
e-mail
• M. Carmen Romero-MorenoDepartamento de Análisis Matemático