On the invariant translation approximation property for discrete groups
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- by Joachim Zacharias PDF
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Abstract:
Recently J. Roe considered the question of whether for a discrete group the reduced group $C^*$-algebra $C_r^*(\Gamma )$ is the fixed point algebra of $\{\text {Ad}(\rho _t) \mid t \in \Gamma \}$ acting on the uniform Roe algebra $UC_r^*(\Gamma )$. $\Gamma$ is said to have the invariant translation approximation property in this case. We consider a slight generalization of this property which, for exact $\Gamma$, is equivalent to the operator space approximation property of $C_r^*(\Gamma )$. We also give a new characterization of exactness and a short proof of the equivalence of exactness of $\Gamma$ and exactness of $C_r^*(\Gamma )$ for discrete groups.References
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Additional Information
- Joachim Zacharias
- Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Email: jz@maths.nott.ac.uk
- Received by editor(s): March 22, 2004
- Received by editor(s) in revised form: February 1, 2005
- Published electronically: January 31, 2006
- Communicated by: David R. Larson
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1909-1916
- MSC (2000): Primary 46L06, 46L85, 20F69
- DOI: https://doi.org/10.1090/S0002-9939-06-08191-3
- MathSciNet review: 2215118