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Residually finite actions and crossed products

Published online by Cambridge University Press:  17 October 2011

DAVID KERR  and
PIOTR W. NOWAK
DAVID KERR
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA (email: [email protected], [email protected])
PIOTR W. NOWAK
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA (email: [email protected], [email protected])
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Abstract

We study a notion of residual finiteness for continuous actions of discrete groups on compact Hausdorff spaces and how it relates to the existence of norm microstates for the reduced crossed product. Our main result asserts that an action of a free group on a zero-dimensional compact metrizable space is residually finite if and only if its reduced crossed product admits norm microstates, i.e., is an MF algebra.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 5 , October 2012 , pp. 1585 - 1614
Copyright
Copyright © Cambridge University Press 2011

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