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arXiv · 1302.5789

Negative definite functions and a dynamical characterization of property (T) for countable groups

Guyan Robertson·Tim Steger
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Abstract

A class of negative definite kernels is defined in terms of measure spaces. Using this concept, property (T) for a countable group $\G$ is characterized in terms of measure preserving actions of $\G$, as follows. If a set $S$ is translated a finite amount by any fixed element of $\G$, then there is a uniform bound on how far $S$ is translated.

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Guyan Robertson, Tim Steger. 2013-02-23. Negative definite functions and a dynamical characterization of property (T) for countable groups. https://arxiv.org/abs/1302.5789

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