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Bibliographic Details
Main Authors: Ferenczi, Valentin, Kaufmann, Pedro L., Pernecká, Eva
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2501.06984
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Table of 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.