Hypercyclic, topologically mixing and chaotic semigroups
on Banach spaces
Studia Mathematica, Tome 170 (2005) no. 1, pp. 57-75
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
paper prove every separable infinite dimensional complex banach space admits topologically mixing holomorphic uniformly continuous semigroup characterize mixing property semigroups operators concrete characterization being topologically mixing translation semigroup weighted spaces functions given moreover prove there exists commutative algebra operators containing chaotic operator operator which multiple identity multiple which chaotic gives negative answer question delaubenfels emamirad
Affiliations des auteurs :
Teresa Bermúdez 1 ; Antonio Bonilla 1 ; José A. Conejero 2 ; Alfredo Peris 3
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author = {Teresa Berm\'udez and Antonio Bonilla and Jos\'e A. Conejero and Alfredo Peris},
title = {Hypercyclic, topologically mixing and chaotic semigroups
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journal = {Studia Mathematica},
pages = {57--75},
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volume = {170},
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year = {2005},
doi = {10.4064/sm170-1-3},
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Teresa Bermúdez; Antonio Bonilla; José A. Conejero; Alfredo Peris. Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces. Studia Mathematica, Tome 170 (2005) no. 1, pp. 57-75. doi: 10.4064/sm170-1-3
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