Supercyclicity in the operator algebra

Alfonso Montes-Rodríguez ¹   ; M. Carmen Romero-Moreno ¹

¹ Departamento de Análisis Matemático Facultad de Matemáticas Universidad de Sevilla Aptdo. 1160 41080 Sevilla, Spain

Studia Mathematica, Tome 150 (2002) no. 3, pp. 201-213

Résumé

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.

Détail

DOI : 10.4064/sm150-3-1

Keywords: prove supercyclicity criterion continuous linear mapping defined operator algebra separable banach space cal result extends recent result hypercyclicity operator algebra hilbert space kind result powerful tool analyze structure supercyclic vectors supercyclic operator defined cal instance consequence main result simple proof recently established certain supercyclic operators defined banach space have infinite dimensional closed subspace supercyclic vectors