Lipschitz-Free Spaces: A Topometric Approach and Group Actions

Michael Megrelishvili

doi:10.1007/s00009-025-02967-3

Lipschitz-Free Spaces: A Topometric Approach and Group Actions

Michael Megrelishvili

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 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 Lip0(M)=F(M)∗ and the bidual F(M)∗∗.

Original language	English
Article number	202
Journal	Mediterranean Journal of Mathematics
Volume	22
Issue number	8
DOIs	https://doi.org/10.1007/s00009-025-02967-3
State	Published - Dec 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Keywords

Arens–Eells embedding
Gromov compactification
Lipschitz-free space
stable Banach space
topometric space

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10.1007/s00009-025-02967-3

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AB - 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 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 Lip0(M)=F(M)∗ and the bidual F(M)∗∗.

KW - Arens–Eells embedding

KW - Gromov compactification

KW - Lipschitz-free space

KW - stable Banach space

KW - topometric space

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Lipschitz-Free Spaces: A Topometric Approach and Group Actions

Abstract

Bibliographical note

Keywords

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