Geodesic
Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces
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
Studia Mathematica, Tome 170 (2005) no. 1, pp. 57-75 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm170-1-3
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

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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     title = {Hypercyclic, topologically mixing and chaotic semigroups
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     journal = {Studia Mathematica},
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 on Banach spaces
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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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