Artículo
Total and non-total suborbits for hypercyclic operators
Autor/es | Bernal González, Luis
Bonilla, Antonio |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2022-11-11 |
Fecha de depósito | 2023-04-17 |
Publicado en |
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Resumen | 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 ... 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. |
Cita | Bernal González, L. y Bonilla, A. (2022). Total and non-total suborbits for hypercyclic operators. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 117, 17-1. https://doi.org/10.1007/s13398-022-01351-0. |