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arXiv · 2506.06770

Almost-invariant elements of group actions on Lip$_0$ spaces

Tomáš Raunig
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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.

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Tomáš Raunig. 2025-06-07. Almost-invariant elements of group actions on Lip$_0$ spaces. https://arxiv.org/abs/2506.06770

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