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Hypercyclic and topologically mixing cosine functions on Banach spaces
Author(s):
Antonio
Bonilla;
Pedro
J.
Miana
Journal:
Proc. Amer. Math. Soc.
136
(2008),
519-528.
MSC (2000):
Primary 47D09, 47A16
Posted:
October 24, 2007
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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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
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