Existence and nonexistence of hypercyclic semigroups
In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from –and considerably shorter than– the one recently given by Bermúdez, Bonilla and Martinón. We also show the...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87518 |
| Acceso en línea: | https://hdl.handle.net/11441/87518 https://doi.org/10.1090/S0002-9939-06-08524-8 |
| Access Level: | acceso abierto |
| Palabra clave: | Hypercyclic uniformly continuous semigroup of operators Topologically mixing semigroup Hypercyclicity criterion Supercyclic semigroup |
| Sumario: | In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional 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. |
|---|