Weak property $(\mathrm{T}_{L^p})$ for discrete groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910358575251456 |
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| author | Elkiær, Emilie Mai |
| author_facet | Elkiær, Emilie Mai |
| contents | We show that, for a countable discrete group $Γ$, property $(\mathrm{T}_{L^p})$ of Bader, Furman, Gelander and Monod is equivalent to the property that, whenever an $L^p$-representation of $Γ$ admits a net of almost invariant unit vectors, it has a non-zero invariant vector. Central in the proof is to show that the closure of the group of $\mathbb{T}$-valued $1$-coboundaries is a sufficient criteria for strong ergodicity of ergodic p.m.p. actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak property $(\mathrm{T}_{L^p})$ for discrete groups Elkiær, Emilie Mai Functional Analysis Group Theory We show that, for a countable discrete group $Γ$, property $(\mathrm{T}_{L^p})$ of Bader, Furman, Gelander and Monod is equivalent to the property that, whenever an $L^p$-representation of $Γ$ admits a net of almost invariant unit vectors, it has a non-zero invariant vector. Central in the proof is to show that the closure of the group of $\mathbb{T}$-valued $1$-coboundaries is a sufficient criteria for strong ergodicity of ergodic p.m.p. actions. |
| title | Weak property $(\mathrm{T}_{L^p})$ for discrete groups |
| topic | Functional Analysis Group Theory |
| url | https://arxiv.org/abs/2403.05312 |