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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.06984 |
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| _version_ | 1866908502851584000 |
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| author | Ferenczi, Valentin Kaufmann, Pedro L. Pernecká, Eva |
| author_facet | Ferenczi, Valentin Kaufmann, Pedro L. Pernecká, Eva |
| contents | We consider Banach spaces $X$ that can be linearly lifted into their Lipschitz-free spaces $\mathcal{F}(X)$ and, for a group $G$ acting on $X$ by linear isometries, we study the possible existence of $G$-equivariant linear liftings. In particular, we prove that such lifting exists when $G$ is compact in the strong operator topology, or an increasing union of such groups and $\mathcal{F}(X)$ is complemented in its bidual by an equivariant projection. As an example of application, we define and study a complex version of the Lipschitz-free space $\mathcal{F}(X)$ when $X$ is a subset of a complex Banach space stable under the action of the circle group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant liftings in Lipschitz-free spaces Ferenczi, Valentin Kaufmann, Pedro L. Pernecká, Eva Functional Analysis We consider Banach spaces $X$ that can be linearly lifted into their Lipschitz-free spaces $\mathcal{F}(X)$ and, for a group $G$ acting on $X$ by linear isometries, we study the possible existence of $G$-equivariant linear liftings. In particular, we prove that such lifting exists when $G$ is compact in the strong operator topology, or an increasing union of such groups and $\mathcal{F}(X)$ is complemented in its bidual by an equivariant projection. As an example of application, we define and study a complex version of the Lipschitz-free space $\mathcal{F}(X)$ when $X$ is a subset of a complex Banach space stable under the action of the circle group. |
| title | Equivariant liftings in Lipschitz-free spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2501.06984 |