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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-3,
author = {Teresa Berm\'udez and Antonio Bonilla and Jos\'e A. Conejero and Alfredo Peris},
title = {Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {57-75},
zbl = {1064.47006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-3}
}
Teresa Bermúdez; Antonio Bonilla; José A. Conejero; Alfredo Peris. Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces. Studia Mathematica, Tome 166 (2005) pp. 57-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-3/