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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the existence of chaotic and hypercyclic semigroups on Banach spaces


Authors: Teresa Bermúdez, Antonio Bonilla and Antonio Martinón
Journal: Proc. Amer. Math. Soc. 131 (2003), 2435-2441
MSC (2000): Primary 47A16, 47D03
Published electronically: November 13, 2002
MathSciNet review: 1974641
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Abstract: We prove that every separable infinite dimensional complex Banach space admits a hypercyclic uniformly continuous semigroup. We also prove that there exist Banach spaces admitting no chaotic strongly continuous semigroups.


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Additional Information

Teresa Bermúdez
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
Email: tbermude@ull.es

Antonio Bonilla
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
Email: abonilla@ull.es

Antonio Martinón
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
Email: anmarce@ull.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06762-X
PII: S 0002-9939(02)06762-X
Keywords: Chaotic semigroup, hypercyclic semigroup, hereditarily indecomposable space.
Received by editor(s): December 8, 2001
Received by editor(s) in revised form: March 11, 2002
Published electronically: November 13, 2002
Additional Notes: The first author was supported in part by Consejería de Educación del Gobierno de Canarias PI 2001/039 (Spain) and Universidad de La Laguna, ref:1802010204.
The second author was supported in part by DGESIC Grant PB 98-0444 (Spain) and by Consejería de Educación del Gobierno de Canarias PI 1999/105 (Spain).
The third author was supported in part by Consejería de Educación del Gobierno de Canarias PI 2001/039 (Spain).
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society