Dense Lineable Criterion for Linear Dynamics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909478587203584 |
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| author | Arbieto, Alexander Saavedra, Manuel |
| author_facet | Arbieto, Alexander Saavedra, Manuel |
| contents | We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos. We show that in every infinite-dimensional separable complex Banach space, there exists a sequence of operators with a dense set of irregular vectors but without a dense irregular manifold, and we exhibit a recurrent operator whose set of recurrent vectors is not dense-lineable. This resolves in the negative a question posed by Grivaux et al. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dense Lineable Criterion for Linear Dynamics Arbieto, Alexander Saavedra, Manuel Functional Analysis Dynamical Systems 47A16, 37B20, 37B02 We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos. We show that in every infinite-dimensional separable complex Banach space, there exists a sequence of operators with a dense set of irregular vectors but without a dense irregular manifold, and we exhibit a recurrent operator whose set of recurrent vectors is not dense-lineable. This resolves in the negative a question posed by Grivaux et al. |
| title | Dense Lineable Criterion for Linear Dynamics |
| topic | Functional Analysis Dynamical Systems 47A16, 37B20, 37B02 |
| url | https://arxiv.org/abs/2502.03352 |