A lifting theorem for operators on spaces of Lipschitz functions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914527514198016 |
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| author | Candido, Leandro |
| author_facet | Candido, Leandro |
| contents | We prove that every bounded linear operator between Lipschitz spaces admits a lifting along the De Leeuw embedding. More precisely, given pointed metric spaces $M$ and $N$ and $ε>0$, every bounded linear operator $S:\mathrm{Lip}_0(M)\to \mathrm{Lip}_0(N)$ admits a lifting $\mathfrak{S}:C(β\tilde{M})\to C(β\tilde{N})$ such that $\|\mathfrak{S}\|\leq \|S\|+ε$ and $\mathfrak{S}(\varPhi_M(f))=\varPhi_N(S(f))$ for every $f\in \mathrm{Lip}_0(M)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02118 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A lifting theorem for operators on spaces of Lipschitz functions Candido, Leandro Functional Analysis We prove that every bounded linear operator between Lipschitz spaces admits a lifting along the De Leeuw embedding. More precisely, given pointed metric spaces $M$ and $N$ and $ε>0$, every bounded linear operator $S:\mathrm{Lip}_0(M)\to \mathrm{Lip}_0(N)$ admits a lifting $\mathfrak{S}:C(β\tilde{M})\to C(β\tilde{N})$ such that $\|\mathfrak{S}\|\leq \|S\|+ε$ and $\mathfrak{S}(\varPhi_M(f))=\varPhi_N(S(f))$ for every $f\in \mathrm{Lip}_0(M)$. |
| title | A lifting theorem for operators on spaces of Lipschitz functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2605.02118 |