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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 and topologically mixing cosine functions on Banach spaces


Authors: Antonio Bonilla and Pedro J. Miana
Journal: Proc. Amer. Math. Soc. 136 (2008), 519-528
MSC (2000): Primary 47D09, 47A16
Published electronically: October 24, 2007
MathSciNet review: 2358492
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Abstract: Our first aim in this paper is to give sufficient conditions for the hypercyclicity and topological mixing of a strongly continuous cosine function. We apply these results to study the cosine function associated to translation groups. We also prove that every separable infinite dimensional complex Banach space admits a topologically mixing uniformly continuous cosine family.


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Additional Information

Antonio Bonilla
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
Email: abonilla@ull.es

Pedro J. Miana
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: pjmiana@unizar.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09036-3
PII: S 0002-9939(07)09036-3
Keywords: Hypercyclic operators, topologically mixing operators, cosine functions, translation groups.
Received by editor(s): July 17, 2006
Published electronically: October 24, 2007
Additional Notes: The first author is supported by MEC and FEDER MTM2005-07347 and MEC (Accion special) MTM2006-26627-E
The second author is supported by Project MTM2004-03036, DGI-FEDER, of the MCYT, Spain, and Project E-64, D.\ G.\ Aragón, Spain.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2007 American Mathematical Society