March 8, 2024Open Access

Weak property (T₋㵵) for discrete groups

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Abstract

We show that, for a countable discrete group, property (T₋㵵) of Bader, Furman, Gelander and Monod is equivalent to the property that, whenever an Lᵖ-representation of 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 T-valued 1-coboundaries is a sufficient criteria for strong ergodicity of ergodic p. m. p. actions.

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Emilie Elkiær (Fri,) studied this question.

synapsesocial.com/papers/68e752dab6db6435876cb713 https://doi.org/https://doi.org/10.48550/arxiv.2403.05312

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