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

 

Hypercyclicity of weighted convolution operators on homogeneous spaces


Authors: C. Chen and C-H. Chu
Journal: Proc. Amer. Math. Soc. 137 (2009), 2709-2718
MSC (2000): Primary 47A16, 47B37, 47B38, 43A85, 44A35
Published electronically: March 10, 2009
MathSciNet review: 2497483
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Abstract: Let $ 1\leq p < \infty$. We show that a weighted translation operator on the $ L^p$ space of a homogeneous space is hypercyclic under some condition on the weight. This condition is also necessary in the discrete case and is equivalent to hereditary hypercyclicity of the operator. The condition can be strengthened to characterise topologically mixing weighted translation operators on discrete spaces.


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Additional Information

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

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

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09889-X
PII: S 0002-9939(09)09889-X
Keywords: Hypercyclic operator, topologically mixing operator, convolution, homogeneous space, $L^p$-space
Received by editor(s): October 28, 2008
Published electronically: March 10, 2009
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.