Lipschitz-Free Spaces: A Topometric Approach and Group Actions

2024/08/27 by Michael Megrelishvili, Megrelishvili, Michael · 1 citation
Mathematics · #43A65 #46B04 #46B20 #51F30 #53C23 #54H15 #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2408.15208

openalex publication_date 2024/08/27 · openalex created_date 2024/09/21 · openalex updated_date 2026/07/28

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)^**.

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• Metric functionals and weak convergence

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