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Isometric actions and finite approximations

Part of: Special aspects of infinite or finite groups Topological dynamics Linear spaces and algebras of operators

Published online by Cambridge University Press:  06 June 2022

S. J. PILGRIM Open the ORCID record for S. J. PILGRIM [Opens in a new window]
S. J. PILGRIM*
Affiliation:
Department of Mathematics, The University of Hawai’i at Mānoa, Honolulu, USA
*
e-mail: spilgrim@hawaii.edu
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Abstract

We show that every isometric action on a Cantor set is conjugate to an inverse limit of actions on finite sets; and that every faithful isometric action by a finitely generated amenable group is residually finite.

Keywords

group actionsoperator algebrasquasidiagonalresidually finite

MSC classification

Primary: 37B99: None of the above, but in this section
Secondary: 47L65: Crossed product algebras (analytic crossed products) 20F65: Geometric group theory
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 7 , July 2023 , pp. 2464 - 2470
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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