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

 

Hypercyclic weighted translations on groups


Authors: C. Chen and C-H. Chu
Journal: Proc. Amer. Math. Soc. 139 (2011), 2839-2846
MSC (2010): Primary 47A16, 47B37, 47B38, 44A35, 43A15
Published electronically: January 6, 2011
MathSciNet review: 2801625
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Abstract: Let $ G$ be a locally compact group and let $ 1\leq p < \infty$. We characterize hypercyclic weighted translation operators on the Lebesgue space $ L^p(G)$ in terms of the weight, extending a recent result by the authors for discrete groups. Topologically mixing weighted translations are also characterized.


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Additional Information

C. Chen
Affiliation: School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom
Email: c.chen@qmul.ac.uk

C-H. Chu
Affiliation: School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom
Email: c.chu@qmul.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10718-4
PII: S 0002-9939(2011)10718-4
Keywords: Hypercyclic operator, topologically mixing operator, convolution, locally compact group, $L^{p}$-space.
Received by editor(s): October 7, 2009
Received by editor(s) in revised form: July 28, 2010
Published electronically: January 6, 2011
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.