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arXiv · 2403.05312

Weak property $(\mathrm{T}_{L^p})$ for discrete groups

Emilie Mai Elkiær
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Abstract

We show that, for a countable discrete group $\Gamma$, property $(\mathrm{T}_{L^p})$ of Bader, Furman, Gelander and Monod is equivalent to the property that, whenever an $L^p$-representation of $\Gamma$ 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.

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Emilie Mai Elkiær. 2024-03-08. Weak property $(\mathrm{T}_{L^p})$ for discrete groups. https://arxiv.org/abs/2403.05312

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