Lipschitz extensions of linear operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908411330822144 |
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| author | Albarracín, Nahuel Turco, Pablo |
| author_facet | Albarracín, Nahuel Turco, Pablo |
| contents | Let $E, F, E_0$ be Banach spaces, with $E_0$ a subspace of $E$. For a maximal Banach operator ideal $\mathcal{A}$, we show that a linear operator from $E_0$ to $F$ can be extended to a linear operator from $E$ to $F$ that belongs to $\mathcal{A}$ if and only if it can be extended to a Lipschitz map from $E$ to $F$ belonging to a wide class of Lipschitz Banach operator ideals related with $\mathcal{A}$. As a consequence, we show that linear operators with special Lipschitz factorization through $\ell_{\infty}(Γ)$ has analogous linear factorization through $\ell_{\infty}(Γ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz extensions of linear operators Albarracín, Nahuel Turco, Pablo Functional Analysis Primary: 46A22, 46A32. Secondary: 47L20, 46B28 Let $E, F, E_0$ be Banach spaces, with $E_0$ a subspace of $E$. For a maximal Banach operator ideal $\mathcal{A}$, we show that a linear operator from $E_0$ to $F$ can be extended to a linear operator from $E$ to $F$ that belongs to $\mathcal{A}$ if and only if it can be extended to a Lipschitz map from $E$ to $F$ belonging to a wide class of Lipschitz Banach operator ideals related with $\mathcal{A}$. As a consequence, we show that linear operators with special Lipschitz factorization through $\ell_{\infty}(Γ)$ has analogous linear factorization through $\ell_{\infty}(Γ)$. |
| title | Lipschitz extensions of linear operators |
| topic | Functional Analysis Primary: 46A22, 46A32. Secondary: 47L20, 46B28 |
| url | https://arxiv.org/abs/2506.14924 |