On the existence of chaotic and hypercyclic semigroups on Banach spaces

Bermúdez, Teresa; Bonilla, Antonio; Martinón, Antonio

doi:10.1090/S0002-9939-02-06762-X

On the existence of chaotic and hypercyclic semigroups on Banach spaces
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by Teresa Bermúdez, Antonio Bonilla and Antonio Martinón

Proc. Amer. Math. Soc. 131 (2003), 2435-2441

DOI: https://doi.org/10.1090/S0002-9939-02-06762-X

Published electronically: November 13, 2002

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Abstract:

We prove that every separable infinite dimensional complex Banach space admits a hypercyclic uniformly continuous semigroup. We also prove that there exist Banach spaces admitting no chaotic strongly continuous semigroups.

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