Hypercyclic semigroups and somewhere dense orbits

George Costakis; Alfredo Peris

doi:10.1016/S1631-073X(02)02572-4

Hypercyclic semigroups and somewhere dense orbits
[Semigroupes hypercycliques et orbites quelque part denses]

George Costakis ¹ ; Alfredo Peris ²

¹ Department of Mathematics, University of Maryland, College Park, MA 20742, USA
² Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, 46071 Valencia, Spain

Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 895-898.

Abstract (VO)
Résumé

We study hypercyclicity of linear strongly continuous semigroups. In the case of iterations of a single operator Bourdon and Feldman have recently proved that the existence of somewhere dense orbits implies hypercyclicity. We show the corresponding result for semigroups. As a consequence, a conjecture of Herrero concerning iterations of a single operator also holds for strongly continuous semigroups.

Nous étudions l'hypercyclicité des semigroupes linéaires et fortement continus. En ce qui concerne l'iteration d'un opérateur, Bourdon et Feldman ont montré que l'existence des orbites quelque part denses implique hypercyclicité. Nous démontrons le resultat correspondant pour des semigroupes. Une conséquence est la generalisation d'une conjecture de Herrero à des semigroupes.

Reçu le : 2001-05-08
Accepté le : 2002-10-03
Publié le : 2002-10-20

DOI : 10.1016/S1631-073X(02)02572-4

Affiliations des auteurs :

George Costakis ¹ ; Alfredo Peris ²

¹ Department of Mathematics, University of Maryland, College Park, MA 20742, USA
² Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, 46071 Valencia, Spain

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George Costakis; Alfredo Peris. Hypercyclic semigroups and somewhere dense orbits. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 895-898. doi : 10.1016/S1631-073X(02)02572-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02572-4/

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Cité par

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