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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Common hypercyclic vectors for families of operators


Authors: Eva A. Gallardo-Gutierrez and Jonathan R. Partington
Journal: Proc. Amer. Math. Soc. 136 (2008), 119-126
MSC (2000): Primary 47A16; Secondary 47B33, 47B37
Published electronically: September 25, 2007
MathSciNet review: 2350396
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Abstract: We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy space, generalizing recent results by Abakumov and Gordon and also Bayart. The criterion is applied to other specific families of operators.


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Additional Information

Eva A. Gallardo-Gutierrez
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza e IUMA, Plaza San Francisco s/n, 50009 Zaragoza, Spain
Email: eva@unizar.es

Jonathan R. Partington
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
Email: J.R.Partington@leeds.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09053-3
PII: S 0002-9939(07)09053-3
Received by editor(s): August 15, 2006
Published electronically: September 25, 2007
Additional Notes: This work was partially supported by Plan Nacional I+D grant no.\ MTM2006-06431, Gobierno de Aragón research group Análisis Matemático y Aplicaciones, ref.\ DGA E-64 and a Scheme 4 grant from the London Mathematical Society
Communicated by: Joseph Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.