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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hypercyclic and topologically mixing cosine functions on Banach spaces
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by Antonio Bonilla and Pedro J. Miana PDF
Proc. Amer. Math. Soc. 136 (2008), 519-528 Request permission


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:
  • Pedro J. Miana
  • Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
  • MR Author ID: 672733
  • Email:
  • 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
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 519-528
  • MSC (2000): Primary 47D09, 47A16
  • DOI:
  • MathSciNet review: 2358492