This paper was in the 2% most cited papers of WoS in the two years after its publication.
Our aim in this paper is to prove that every separable infinite-dimensional complex Banach space admits a topologically mixing holomorphic uniformly continuous semigroup and to characterize the mixing property for semigroups of operators. A concrete characterization of being topologically mixing for the translation semigroup on weighted spaces of functions is also given. Moreover, we prove that there exists a commutative algebra of operators containing both a chaotic operator and an operator which is not a multiple of the identity and no multiple of which is chaotic. This gives a negative answer to a question of deLaubenfels and Emamirad.
T. Bermúdez, A. Bonilla, J. A. Conejero, and A. Peris. Hypercyclic, topologically mixing and chaotic semi- groups on Banach spaces. Studia Math., 170(1):57–75, 2005. doi:10.4064/sm170-1-3
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