1Departamento de Análisis Matemático Universidad de La Laguna E-38271 La Laguna (Tenerife), Spain 2Facultat d'Informàtica Departament de Matemàtica Aplicada and IMPA Universitat Politècnica de València E-46022 València, Spain 3E.T.S. Arquitectura Departament de Matemàtica Aplicada and IMPA Universitat Politècnica de València E-46022 València, Spain
Studia Mathematica, Tome 170 (2005) no. 1, pp. 57-75
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
1
Departamento de Análisis Matemático Universidad de La Laguna E-38271 La Laguna (Tenerife), Spain
2
Facultat d'Informàtica Departament de Matemàtica Aplicada and IMPA Universitat Politècnica de València E-46022 València, Spain
3
E.T.S. Arquitectura Departament de Matemàtica Aplicada and IMPA Universitat Politècnica de València E-46022 València, Spain
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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
on {Banach} spaces},
journal = {Studia Mathematica},
pages = {57--75},
year = {2005},
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number = {1},
doi = {10.4064/sm170-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm170-1-3/}
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AU - Teresa Bermúdez
AU - Antonio Bonilla
AU - José A. Conejero
AU - Alfredo Peris
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JO - Studia Mathematica
PY - 2005
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%A Teresa Bermúdez
%A Antonio Bonilla
%A José A. Conejero
%A Alfredo Peris
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on Banach spaces
%J Studia Mathematica
%D 2005
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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
