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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.14808 |
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| _version_ | 1866908539070447616 |
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| author | Fu, Xiangdi Guo, Kunyu Li, Dilong |
| author_facet | Fu, Xiangdi Guo, Kunyu Li, Dilong |
| contents | Through the establishment of several extension theorems, we provide explicit expressions for all contractive projections and 1-complemented subspaces in the Hardy space $H^p(\mathbb{T})$ for $1\leq p<\infty$, $p\neq 2$. Our characterization leads to two corollaries: first, all nontrivial 1-complemented subspaces of $H^p(\mathbb{T})$ are isometric to $H^p(\mathbb{T})$; second, all contractive projections on $H^p(\mathbb{T})$ are restrictions of contractive projections on $L^p(\mathbb{T})$ that leave $H^p(\mathbb{T})$ invariant. The first corollary provides examples of prime Banach spaces \emph{in the isometric sense}, while the second answers a question posed by P. Wojtaszczyk in 2003. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14808 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extension of contractive projections Fu, Xiangdi Guo, Kunyu Li, Dilong Functional Analysis Through the establishment of several extension theorems, we provide explicit expressions for all contractive projections and 1-complemented subspaces in the Hardy space $H^p(\mathbb{T})$ for $1\leq p<\infty$, $p\neq 2$. Our characterization leads to two corollaries: first, all nontrivial 1-complemented subspaces of $H^p(\mathbb{T})$ are isometric to $H^p(\mathbb{T})$; second, all contractive projections on $H^p(\mathbb{T})$ are restrictions of contractive projections on $L^p(\mathbb{T})$ that leave $H^p(\mathbb{T})$ invariant. The first corollary provides examples of prime Banach spaces \emph{in the isometric sense}, while the second answers a question posed by P. Wojtaszczyk in 2003. |
| title | Extension of contractive projections |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2412.14808 |