Hostname: page-component-84b7d79bbc-g5fl4 Total loading time: 0 Render date: 2024-07-28T23:18:15.770Z Has data issue: false hasContentIssue false
  • English
  • Français

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: guyan@maths.newcastle.edu.au)
TIM STEGER
Affiliation:
Istituto di Matematica e Fisica, Università di Sassari, via Vienna 2, 07100 Sassari, Italy (e-mail: steger@ssmain.uniss.it)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was supported by the Australian Research Council.