Beurling and Model subspaces invariant under a universal operator
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909223517945856 |
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| author | Eidt, Ben Hur Noor, S. Waleed |
| author_facet | Eidt, Ben Hur Noor, S. Waleed |
| contents | In this article, we characterize the Beurling and Model subspaces of the Hardy-Hilbert space $H^2(\mathbb{D})$ invariant under the composition operator $C_{ϕ_a}f=f\circϕ_a$, where $ϕ_a(z) = az + 1 - a$ for $a \in (0,1)$ is an affine self-map of the open unit disk $\mathbb{D}$. These operators have universal translates (in the sense of Rota) and have attracted attention recently due to their connection with the Invariant Subspace Problem (ISP) and the classical Cesàro operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Beurling and Model subspaces invariant under a universal operator Eidt, Ben Hur Noor, S. Waleed Functional Analysis In this article, we characterize the Beurling and Model subspaces of the Hardy-Hilbert space $H^2(\mathbb{D})$ invariant under the composition operator $C_{ϕ_a}f=f\circϕ_a$, where $ϕ_a(z) = az + 1 - a$ for $a \in (0,1)$ is an affine self-map of the open unit disk $\mathbb{D}$. These operators have universal translates (in the sense of Rota) and have attracted attention recently due to their connection with the Invariant Subspace Problem (ISP) and the classical Cesàro operator. |
| title | Beurling and Model subspaces invariant under a universal operator |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2406.07774 |