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arXiv · 2408.15208

Lipschitz-Free Spaces: A Topometric Approach and Group Actions

Michael Megrelishvili
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Abstract

We introduce a topometric version of Lipschitz-free spaces and study its universal property. Another aim of this paper is to investigate actions of topological groups $G$ on Lipschitz-free spaces $\mathcal{F}(M)$, induced by isometric actions on pointed metric spaces $M$. In particular, we study the associated dynamical $G$-systems under the weak-star topology, focusing on the dual action on $\mathrm{Lip}_0(M) = \mathcal{F}(M)^*$ and the bidual $\mathcal{F}(M)^{**}$.

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BibTeXRIS

Michael Megrelishvili. 2024-08-27. Lipschitz-Free Spaces: A Topometric Approach and Group Actions. https://arxiv.org/abs/2408.15208

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