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

Published online by Cambridge University Press:  01 February 1998

GUYAN ROBERTSON  and
TIM STEGER
GUYAN ROBERTSON
Affiliation:
Department of Mathematics, University of Newcastle, NSW 2308, Australia (e-mail: [email protected])
TIM STEGER
Affiliation:
Istituto di Matematica e Fisica, Università di Sassari, via Vienna 2, 07100 Sassari, Italy (e-mail: [email protected])
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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 $\Gamma$ is characterized in terms of measure-preserving actions of $\Gamma$, as follows. If a set $S$ is translated a finite amount by any fixed element of $\Gamma$, then there is a uniform bound on how far $S$ is translated.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 1 , February 1998 , pp. 247 - 253
Copyright
1998 Cambridge University Press

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Footnotes

This research was supported by the Australian Research Council.