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Bulletin of the London Mathematical Society Advance Access originally published online on July 14, 2009
Bulletin of the London Mathematical Society 2009 41(5):823-830; doi:10.1112/blms/bdp055
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© 2009 London Mathematical Society

Semigroups of chaotic operators

Frédéric Bayart

Laboratoire de Mathématiques
UMR6620
Université Blaise Pascal
63177 Aubiere cedex
France
Frederic.Bayart@math.univ-bpclermont.fr

Teresa Bermúdez

Departamento de Análisis Matemático
Universidad de La Laguna
38271 La Laguna
Tenerife
Spain

Received 6 February 2008. Revision received 7 October 2008.

We prove the existence of chaotic semigroups of operators that do not contain any chaotic operator. In particular, we obtain a chaotic operator T such that {lambda} T is not chaotic for some unimodular complex number {lambda}.

The first author was partly supported by ANR Dynop. The second author was supported by Ministerio de Educación y Ciencia (Spain), MTM2007-6560.

2000 Mathematics Subject Classification 47A16.


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