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On some “stability” properties of the full C*-algebra associated to the free group F∞

Published online by Cambridge University Press:  20 January 2009

Asma Harcharras
Asma Harcharras
Affiliation:
Université Paris, 6 Équipe D'analyse, Case 186 75252 Paris Cedex 05, France, E-mail address: harchars@moka.ccr.jussieu.fr
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Let C*(F∞) be the full C*-algebra associated to the free group of countably many generators and SnC*(F∞) be the class of all n-dimensional operator subspaces of C*(F∞). In this paper, we study some stability properties of SnC*(F∞). More precisely, we will prove that for any E0, E1 in SnC*(F∞), the Haagerup tensor product E0⊗hE1 and the operator space obtained by complex interpolation Eθ are (1 + ∈)-contained in C*(F∞) for arbitrary ∈>0. On the other hand, we will show an extension property for WEPC*-algebras.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 1 , February 1998 , pp. 93 - 116
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

REFERENCES

1.Bergh, J., On the relation between the two complex methods of interpolation, Indiana Univ. Math. J. 28 (1979), 775–777.CrossRefGoogle Scholar
2.Bergh, J. and Löfström, J., Interpolation spaces. An introduction (Springer Verlag, New York, 1976).Google Scholar
3.Blecher, D., The standard dual of an operator space, Pacific J. Math. 153 (1992), 15–30.CrossRefGoogle Scholar
4.Blecher, D. and Paulsen, V., Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262–292.Google Scholar
5.Choi, M. D. and Effros, E., Injectivity and operator spaces, J. Funct. Anal. 24 (1977), 156–209.CrossRefGoogle Scholar
6.Christensen, E., Effros, E. and Sinclair, A., Completely bounded multilinear maps and C*-algebraic cohomology, Invent. Math. 90 (1987), 279–296.CrossRefGoogle Scholar
7.Cuntz, J., Simple C*-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173–185.Google Scholar
8.De Cannière, J. and Haagerup, U., Multipliers of the Fourier algebras of some simple Lie groups and their discrete subgroups, Amer. J. Math. 107 (1985), 455–500.Google Scholar
9.Dykema, K. J., Nica, A. and Voiculescu, D. V., Free random variables (CRM Monograph Series, Vol I, Amer. Math. Soc., Providence RI).Google Scholar
10.Effros, E. and Haagerup, U., Lifting problems and local reflexivity for C*-algebras, Duke Math. J. 52 (1985), 103–128.Google Scholar
11.Effros, E. and Ruan, Z., On approximation properties for operator spaces, Internat. J. Math. 1 (1990), 163–187.CrossRefGoogle Scholar
12.Effros, E. and Ruan, Z., A new approach to operator spaces. Canad. Math. Bull. 34 (1991), 329–337.Google Scholar
13.Effros, E. and Ruan, Z., Self-duality for the Haagerup tensor product and Hilbert space factorization, J Funct. Anal 100 (1991), 257–284.Google Scholar
14.Guichardet, A., Tensor products of C*-algebras, Soviet Math. Dokl. 6 (1965), 210–213.Google Scholar
15.Haagerup, U., Selfpolar forms, conditional expectations and the weak expectation property for C*-algebras, to appear.Google Scholar
16.Junge, M. and Pisier, G., Bilinear forms on exact operator spaces and B(H)⊗B(H), Geom. Funct. Anal. 5 (1995), 329–363.Google Scholar
17.Kirchberg, E., On non-semisplit extensions, tensor products and exactness of group C*-algebras, Invent. Math. 112 (1993), 449–489.Google Scholar
18.Lance, C., On nuclear C*-algebras, J. Funct. Anal. 12 (1973), 157–176.CrossRefGoogle Scholar
19.Paulsen, V., Completely bounded maps and dilations (Pitman Research Notes 146, Pitman Longman Wiley, 1986).Google Scholar
20.Pisier, G., A simple proof of a theorem of Kirchberg and related results on C*-norms, J. Op. Theory, to appear.Google Scholar
21.Pisier, G., The operator Hilbert space OH, complex interpolation and tensor norms, Mem. Amer. Math. Soc. (1996), to appear.CrossRefGoogle Scholar
22.Pisier, G., Non-commutative vector valued L p-spaces and completely p-summing maps, to appear.Google Scholar
23.Pisier, G., On exact operator spaces, Astérique, to appear.Google Scholar
24.Pisier, G., An introduction to the theory of operator spaces, to appear.Google Scholar
25.Stafney, J., The spectrum of an operator on an interpolation space, Trans. Amer. Math. Soc. 144 (1969), 333–349.Google Scholar
26.Wassermann, S., Exact C*-algebras and related topics (Lect. Notes Series 19, Seoul National University, 1994).Google Scholar