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Bulletin of the London Mathematical Society Advance Access originally published online on December 14, 2006
Bulletin of the London Mathematical Society 2007 39(1):35-38; doi:10.1112/blms/bdl003
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© 2006 London Mathematical Society

Boundaries of reduced free group C*-algebras

Narutaka Ozawa

Department of Mathematical Sciences
University of Tokyo
3-8-1 Komaba
Meguro
Tokyo 153-8914
Japan
Department of Mathematics
UCLA
Los Angeles
CA 90095-1555
USA
narutaka{at}ms.u-tokyo.ac.jp

Received 23 February 2005. Revision received 6 April 2006.

We prove that the crossed product C*-algebra C*r({Gamma}, {partial}{Gamma}) of a free group {Gamma} with its boundary {partial}{Gamma} sits naturally between the reduced group C*-algebra C*r{Gamma} and its injective envelope I(C*r{Gamma}). In other words, we have natural inclusion C*r{Gamma} sub C*r({Gamma}, {partial}{Gamma}) sub I(C*r{Gamma}) of C*-algebras.


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