Frequently hypercyclic composition operators on the little Lipschitz space of a rooted tree
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914430661427200 |
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| author | López-Martínez, Antoni |
| author_facet | López-Martínez, Antoni |
| contents | We characterize the strictly increasing symbols $φ:\mathbb{N}_0\longrightarrow\mathbb{N}_0$ whose composition operators $C_φ$ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space $\mathcal{L}_0(\mathbb{N}_0)$. With this result we continue the recent research about this kind of spaces and operators, but our approach relies on establishing a natural isomorphism between the Lipschitz-type spaces over rooted trees and the classical spaces $\ell^{\infty}$ and $c_0$. Such isomorphism provides an alternative framework that simplifies and allows to improve many previous results about these spaces and the operators defined there. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_02397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frequently hypercyclic composition operators on the little Lipschitz space of a rooted tree López-Martínez, Antoni Functional Analysis Dynamical Systems 47A16, 47B37, 05C05, 05C63 We characterize the strictly increasing symbols $φ:\mathbb{N}_0\longrightarrow\mathbb{N}_0$ whose composition operators $C_φ$ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space $\mathcal{L}_0(\mathbb{N}_0)$. With this result we continue the recent research about this kind of spaces and operators, but our approach relies on establishing a natural isomorphism between the Lipschitz-type spaces over rooted trees and the classical spaces $\ell^{\infty}$ and $c_0$. Such isomorphism provides an alternative framework that simplifies and allows to improve many previous results about these spaces and the operators defined there. |
| title | Frequently hypercyclic composition operators on the little Lipschitz space of a rooted tree |
| topic | Functional Analysis Dynamical Systems 47A16, 47B37, 05C05, 05C63 |
| url | https://arxiv.org/abs/2505.02397 |