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On hypercyclicity and supercyclicity criteria

Published online by Cambridge University Press:  17 April 2009

Teresa Bermúdez ,
Antonio Bonilla  and
Alfredo Peris
Teresa Bermúdez
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain, e-mail: [email protected]
Antonio Bonilla
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain, e-mail: [email protected]
Alfredo Peris
Affiliation:
E.T.S. Arquitectura, Departament de Matemàtica Aplicada, Universitat Politècnica de València, E-46022 València, Spain, e-mail: [email protected]
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 45 - 54
Copyright
Copyright © Australian Mathematical Society 2004

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