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arXiv · 2501.06984

Equivariant liftings in Lipschitz-free spaces

Valentin Ferenczi·Pedro L. Kaufmann·Eva Pernecká
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Abstract

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.

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Valentin Ferenczi, Pedro L. Kaufmann, Eva Pernecká. 2025-01-13. Equivariant liftings in Lipschitz-free spaces. https://arxiv.org/abs/2501.06984

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