Total and non-total suborbits for hypercyclic operators
In this note, it is proved that if X is a separable infinite dimensional Fréchet space that admits a continuous norm then, given a closed infinite dimensional subspace of X, there exists a hypercyclic operator admitting a dense orbit which in turn admits a suborbit all of whose sub-suborbits are tot...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/144475 |
| Acceso en línea: | https://hdl.handle.net/11441/144475 https://doi.org/10.1007/s13398-022-01351-0 |
| Access Level: | acceso abierto |
| Palabra clave: | Orbit under an operator Suborbit Hypercyclic operator Supercyclic operator Total set |
| Sumario: | In this note, it is proved that if X is a separable infinite dimensional Fréchet space that admits a continuous norm then, given a closed infinite dimensional subspace of X, there exists a hypercyclic operator admitting a dense orbit which in turn admits a suborbit all of whose sub-suborbits are total in the prescribed subspace. This is related to a recently published result asserting that every supercyclic vector for an operator on a Hilbert space supports a non-total suborbit. Here we also extend this result to normed spaces. |
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