Hypercyclic subspaces in Fréchet spaces
In this note, we show that every infinite-dimensional separable Fr´echet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of b...
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87517 |
| Acceso en línea: | https://hdl.handle.net/11441/87517 https://doi.org/10.1090/S0002-9939-05-08242-0 |
| Access Level: | acceso abierto |
| Palabra clave: | Hypercyclic operator Hypercyclic sequence Hypercyclic subspace Backward shift Fréchet space |
| Sumario: | In this note, we show that every infinite-dimensional separable Fr´echet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of bounded operators when endowed with the strong operator topology. This completes earlier work of several authors. |
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