Bulletin of the Australian Mathematical Society

Research Article

On hypercyclicity and supercyclicity criteria

Teresa Bermúdeza1, Antonio Bonillaa2 and Alfredo Perisa3

a1 Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain, e-mail: tbermude@ull.es

a2 Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain, e-mail: abonilla@ull.es

a3 E.T.S. Arquitectura, Departament de Matemàtica Aplicada, Universitat Politècnica de València, E-46022 València, Spain, e-mail: aperis@mat.upv.es

We show that the Hypercyclicity Criterion coincides with other existing hypercyclicity criteria and prove that a wide class of hypercyclic operators satisfy the Criterion. The results obtained extend or improve earlier work of several authors. We also unify the different versions of the Supercyclicity Criterion and show that operators with dense generalised kernel and dense range are supercyclic.

(Received October 14 2003)