Compact linear combinations of composition operators on Hardy spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910647504076800 |
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| author | Doubtsov, Evgueni Rutsky, Dmitry V. |
| author_facet | Doubtsov, Evgueni Rutsky, Dmitry V. |
| contents | Let $φ_j$, $j=1,2, \dots, N$, be holomorphic self-maps of the unit disk $\mathbb{D}$ of $\mathbb{C}$. We prove that the compactness of a linear combination of the composition operators $C_{φ_j}: f\mapsto f\circφ_j$ on the Hardy space $H^p(\mathbb{D})$ does not depend on $p$ for $0<p<\infty$. This answers a conjecture of Choe et al. about the compact differences $C_{φ_1} - C_{φ_2}$ on $H^p(\mathbb{D})$, $0<p<\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compact linear combinations of composition operators on Hardy spaces Doubtsov, Evgueni Rutsky, Dmitry V. Complex Variables Functional Analysis Primary 47B33, Secondary 32A35, 46B70, 46M35, 47B07 Let $φ_j$, $j=1,2, \dots, N$, be holomorphic self-maps of the unit disk $\mathbb{D}$ of $\mathbb{C}$. We prove that the compactness of a linear combination of the composition operators $C_{φ_j}: f\mapsto f\circφ_j$ on the Hardy space $H^p(\mathbb{D})$ does not depend on $p$ for $0<p<\infty$. This answers a conjecture of Choe et al. about the compact differences $C_{φ_1} - C_{φ_2}$ on $H^p(\mathbb{D})$, $0<p<\infty$. |
| title | Compact linear combinations of composition operators on Hardy spaces |
| topic | Complex Variables Functional Analysis Primary 47B33, Secondary 32A35, 46B70, 46M35, 47B07 |
| url | https://arxiv.org/abs/2404.14947 |