Almost-invariant elements of group actions on Lip$_0$ spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908398672412672 |
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| author | Raunig, Tomáš |
| author_facet | Raunig, Tomáš |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06770 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost-invariant elements of group actions on Lip$_0$ spaces Raunig, Tomáš Functional Analysis 46B04, 46E15 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. |
| title | Almost-invariant elements of group actions on Lip$_0$ spaces |
| topic | Functional Analysis 46B04, 46E15 |
| url | https://arxiv.org/abs/2506.06770 |