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PURE STATES ON FREE GROUP C*-ALGEBRAS

Published online by Cambridge University Press:  04 December 2009

CHARLES AKEMANN
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA e-mail: [email protected]
SIMON WASSERMANN
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK e-mail: [email protected]
NIK WEAVER
Affiliation:
Department of Mathematics, Washington University in Saint Louis, Saint Louis, MO 63130, USA e-mail: [email protected]
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Abstract

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We prove that all the pure states of the reduced C*-algebra of a free group on an uncountable set of generators are *-automorphism equivalent and extract some consequences of this fact.

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Akemann, C. A., Operator algebras associated with Fuchsian groups, Houston J. Math. 7 (3) (1981), 295301.Google Scholar
2.Akemann, C. A., Anderson, J. and Pedersen, G. K., Excising states of C*-algebras, Canad. J. Math. 38 (5) (1986), 223230.CrossRefGoogle Scholar
3.Akemann, C. A. and Lee, T.-Y., Computing norms in group C*-algebras, Indiana U. Math. J. 29 (4) (1980), 505511.CrossRefGoogle Scholar
4.Akemann, C. A. and Ostrand, P. A., Simple C*-algebras associated with free groups, Amer. J. Math. 98 (4) (1976), 10151047.CrossRefGoogle Scholar
5.Akemann, C. A. and Weaver, N., Classically normal pure states, Positivity.Google Scholar
6.Archbold, R., A mean ergodic theorem associated with the free group on two generators, J. Lond. Math. Soc. 13 (2) (1976), 339345.CrossRefGoogle Scholar
7.Avitsour, D., Free products of C*-algebras, Trans. A.M.S. 271 (1982), 423435.Google Scholar
8.Choi, M.-D., A simple C*-algebra generated by two finite-order unitaries, Canad. J. Math. 21 (1979), 867880.CrossRefGoogle Scholar
9.Kadison, R. V. and Ringrose, J., Fundamentals of the theory of operator algebras, vol. 1 (Academic Press, London, 1983).Google Scholar
10.Kishimoto, A., Ozawa, N. and Sakai, S., Homogeneity of the pure state space of a separable C*-algebra, Canad. Math. Bull. 46 (2003), 365372.CrossRefGoogle Scholar
11.Popa, S., Orthogonal pairs of *-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (183), 253268.Google Scholar
12.Powers, R., Simplicity of the C*-algebra associated with the free group on two generators, Duke Math. J. 42 (1975), 151156.CrossRefGoogle Scholar