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On hypercyclicity and supercyclicity criteria

Published online by Cambridge University Press:  17 April 2009

Teresa Bermúdez
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain, e-mail: tbermude@ull.es
Antonio Bonilla
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain, e-mail: abonilla@ull.es
Alfredo Peris
Affiliation:
E.T.S. Arquitectura, Departament de Matemàtica Aplicada, Universitat Politècnica de València, E-46022 València, Spain, e-mail: aperis@mat.upv.es
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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
Copyright
Copyright © Australian Mathematical Society 2004

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