Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces

Teresa Bermúdez, et al. "Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces." Studia Mathematica 170.1 (2005): 57-75. <http://eudml.org/doc/284900>.

@article{TeresaBermúdez2005,
abstract = {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.},
author = {Teresa Bermúdez, Antonio Bonilla, José A. Conejero, Alfredo Peris},
journal = {Studia Mathematica},
keywords = {one-parameter semigroup; hypercyclicity; chaotic operator; topologically mixing semigroup; generalized backward shift; infinitesimal generators; hereditary indecomposability},
language = {eng},
number = {1},
pages = {57-75},
title = {Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces},
url = {http://eudml.org/doc/284900},
volume = {170},
year = {2005},
}

TY - JOUR
AU - Teresa Bermúdez
AU - Antonio Bonilla
AU - José A. Conejero
AU - Alfredo Peris
TI - Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces
JO - Studia Mathematica
PY - 2005
VL - 170
IS - 1
SP - 57
EP - 75
AB - 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.
LA - eng
KW - one-parameter semigroup; hypercyclicity; chaotic operator; topologically mixing semigroup; generalized backward shift; infinitesimal generators; hereditary indecomposability
UR - http://eudml.org/doc/284900
ER -