Existence and nonexistence of hypercyclic semigroups
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- by L. Bernal-González and K.-G. Grosse-Erdmann PDF
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Abstract:
In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinite-dimensional Banach space that is very different from—and considerably shorter than—the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite-dimensional Fréchet space. This complements recent results due to Bès and Chan. Moreover, we discuss the Hypercyclicity Criterion for semigroups and we give an example of a separable infinite-dimensional locally convex space which supports no supercyclic strongly continuous semigroup of operators.References
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Additional Information
- L. Bernal-González
- Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Apdo. 1160, Avda. Reina Mercedes, 41080 Sevilla, Spain
- Email: lbernal@us.es
- K.-G. Grosse-Erdmann
- Affiliation: Fachbereich Mathematik, Fernuniversität Hagen, 58084 Hagen, Germany
- Email: kg.grosse-erdmann@fernuni-hagen.de
- Received by editor(s): November 29, 2004
- Received by editor(s) in revised form: October 5, 2005
- Published electronically: August 31, 2006
- Additional Notes: The first author was partially supported by Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 and by Ministerio de Ciencia y Tecnología Grant BFM2003-03893-C02-01
- Communicated by: Joseph A. Ball
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 755-766
- MSC (2000): Primary 47A16; Secondary 47D03
- DOI: https://doi.org/10.1090/S0002-9939-06-08524-8
- MathSciNet review: 2262871