Almost-invariant elements of group actions on Lip₀ spaces

2025/06/07 by Tomáš Raunig, Raunig, Tomáš
Mathematics · #46B04 #46E15 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2506.06770

openalex publication_date 2025/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work is motivated by a question published in E. Glasner's paper On a question of Kazhdan and Yom Din regarding the possibility to approximate functionals on a Banach space which are almost invariant with respect to an action of a discrete group by functionals that are invariant. We study the case when the Banach space is a Lipschitz-free space equipped with an action induced by an action by isometries on the underlaying space. We find a few different conditions sufficient for the answer to be positive; for example the case of free or finitely presented groups endowed with left-invariant metrics acting on themselves by translations. Relations to quasimorphisms are also briefly studied.

Citations

• On Lipschitz functions on groups equipped with conjugation-invariant norms
• On a question of Kazhdan and Yom Din

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