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

1998 Ergodic Theory and Dynamical Systems  
A class of negative definite kernels is defined in terms of measure spaces. Using this concept, property (T) for a countable group Γ is characterized in terms of measure preserving actions of Γ, as follows. If a set S is translated a finite amount by any fixed element of Γ, then there is a uniform bound on how far S is translated.
doi:10.1017/s0143385798100342 fatcat:k5bhzf3d6jf3pf7lhu3uhmvuu4