Hypercyclic and topologically mixing cosine functions on Banach spaces

Bonilla, Antonio; Miana, Pedro

doi:10.1090/S0002-9939-07-09036-3

Hypercyclic and topologically mixing cosine functions on Banach spaces
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by Antonio Bonilla and Pedro J. Miana

Proc. Amer. Math. Soc. 136 (2008), 519-528

DOI: https://doi.org/10.1090/S0002-9939-07-09036-3

Published electronically: 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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