Fast orbital convergence reveals more hypercyclic vectors
[EN] Let X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a hypercyclic vector of T. As a corollary,...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/227675 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/227675 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach space Hypercyclic operator Orbital speed Frequent hypercyclicity |
| Sumario: | [EN] Let X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a hypercyclic vector of T. As a corollary, we deduce that if T is a frequently hypercyclic operator with spectral radius r(T) = 1, then lim_{n\to \infty} ∥Tnx∥^{1/n} = 1 for every frequently hypercyclic vector x of T. Some related observations are also made. |
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