Kernels of Bounded Operators on the Classical Transfinite Banach Sequence Spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929762113421312 |
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| author | Arnott, Max Laustsen, Niels Jakob |
| author_facet | Arnott, Max Laustsen, Niels Jakob |
| contents | Every closed subspace of each of the Banach spaces $X = \ell_p(Γ)$ and $X=c_0(Γ)$, where $Γ$ is a set and $1<p<\infty$, is the kernel of a bounded operator $X\to X$.
On the other hand, whenever $Γ$ is an uncountable set, $\ell_1(Γ)$ contains a closed subspace that is not the kernel of any bounded operator $\ell_1(Γ)\to\ell_1(Γ)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_12940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kernels of Bounded Operators on the Classical Transfinite Banach Sequence Spaces Arnott, Max Laustsen, Niels Jakob Functional Analysis 46B26, 46B45, 47B01 (Primary) 18A30, 47A05 (Secondary) Every closed subspace of each of the Banach spaces $X = \ell_p(Γ)$ and $X=c_0(Γ)$, where $Γ$ is a set and $1<p<\infty$, is the kernel of a bounded operator $X\to X$. On the other hand, whenever $Γ$ is an uncountable set, $\ell_1(Γ)$ contains a closed subspace that is not the kernel of any bounded operator $\ell_1(Γ)\to\ell_1(Γ)$. |
| title | Kernels of Bounded Operators on the Classical Transfinite Banach Sequence Spaces |
| topic | Functional Analysis 46B26, 46B45, 47B01 (Primary) 18A30, 47A05 (Secondary) |
| url | https://arxiv.org/abs/2503.12940 |