Khintchine type inequalities for reduced free products and applications

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 599, 2006, Pages 27-59

  Ricard, Éric ^a,b   Hu, Quanhua ^a,b  

^a Université de Franche Comté ^*

^b UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845398212     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/CRELLE.2006.077     Document Type: Article

References (30)

1. Avitzour, D., Free products of C*-algebras, Trans. Amer. Math. Soc. 271, 2 (1982), 423-435.
2. Blanchard, E. F., and Dykema, K. J., Embeddings of reduced free products of operator algebras, Pacific J. Math. 199, 1 (2001), 1-19.
3. Blecher, D., and Le Merdy, C., Operator Algebras and their modules, an operator space approach, Clarendon Press, Oxford 2004.
4. Boca, F., On the method of constructing irreducible finite index subfactors of Popa, Pac. J. Math. 161, 2 (1993), 201-231.
5. Bożejko, M., Positive and negative definite kernels on discrete groups, Lectures at Heidelberg University, 1987.
6. Bożejko, M., Uniformly bounded representations of free groups, J. reine angew. Math. 377 (1987), 170-186.
7. Bożejko, M., and Picardello, M. A., Weakly amenable groups and amalgamated products, Proc. Amer. Math. Soc. 117, 4 (1993), 1039-1046.
8. Buchholz, A., Norm of convolution by operator-valued functions on free groups, Proc. Amer. Math. Soc. 127, 6 (1999), 1671-1682.
9. Cherix, P.-A., Cowling, M., Jolissaint, P., Julg, P., and Valette, A., Groups with the Haagerup property, Gromov's a-T-menability, Progr. Math. 197, Birkhäuser Verlag, Basel 2001.
10. China, W.-M., Free products of von Neumann algebras, Trans. Amer. Math. Soc. 178 (1973), 147-163.
11. Chu, C.-H., von Neumann algebras which are second dual spaces, Proc. Amer. Math. Soc. 112 (1991), 999-1000.
12. Dixmier, J., Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de von Neumann), Les Grands Classiques Gauthier-Villars, Éditions Jacques Gabay, Paris 1996. Reprint of the second (1969) edition.
13. Dykema, K. J., Exactness of reduced amalgamated free product C*-algebras, Forum Math. 16, 2 (2004), 161-180.
14. Dykema, K. J., and Shlyakhtenko, D., Exactness of Cuntz-Pimsner C*-algebras, Proc. Edinb. Math. Soc. (2) 44, 2 (2001), 425-444.
15. Dykema, K. J., and Smith, R. R., Completely bounded approximation property for extended Cuntz-Pimser algebras, Houston J. Math. 31 (2005), 827-840.
16. Effros, E. G., and Ruan, Z.-J., Operator spaces, London Math. Soc. Monogr., New Series 23, The Clarendon Press, Oxford University Press, New York 2000.
17. Effros, E. G., and Ruan, Z.-J., Operator space tensor products and Hopf convolution algebras, J. Oper. Th. 50, 1 (2003), 131-156.
18. Haagerup, U., An example of a nonnuclear C*-algebra, which has the metric approximation property, Invent. Math. 50, 3 (1978/79), 279-293.
19. Haagerup, U., and Kraus, J., Approximation properties for group C*-algebras and group von Neumann algebras, Trans. Amer. Math. Soc. 344, 2 (1994), 667-699.
20. Haagerup, U., and Pisier, G., Bounded linear operators between C*-algebras, Duke Math. J. 71, 3 (1993), 889-925.
21. Jolissaint, P., Haagerup approximation property for finite von Neumann algebras, J. Oper. Th. 48, 3, suppl. (2002), 549-571.
22. Junge, M., Embedding of the operator space OH and the logarithmic 'little Grothendieck inequality', Invent. Math. 161 (2005), 225-286.
23. Junge, M., Parcet, J., Xu, Q., Rosenthal type inequalities for free chaos, in preparation.
24. Leinert, M., Faltungsoperatoren auf gewissen diskreten Gruppen, Stud. Math. 52 (1974), 149-158.
25. Pisier, G., Introduction to operator space theory, London Math. Soc. Lect. Note Ser. 294, Cambridge University Press, Cambridge 2003.
26. Sinclair, A. M., and Smith, R. R., The completely bounded approximation property for discrete crossed products, Indiana Univ. Math. J. 46, 4 (1997), 1311-1322.
27. Voiculescu, D., Symmetries of some reduced free product C*-algebras, in: Operator algebras and their connections with topology and ergodic theory (Buşteni 1983), Lect. Notes Math. 1132, Springer, Berlin (1985), 556-588.
28. Voiculescu, D., A strengthened asymptotic freeness result for random matrices with applications to free entropy, Internat. Math. Res. Notices 1 (1998), 41-63.
29. Voiculescu, D. V., Dykema, K. J., and Nica, A., Free random variables, CRM Monogr. Ser. 1, American Mathematical Society, Providence, RI, 1992.
30. Wysoczański, J., A characterization of radial Herz-Schur multipliers on free products of discrete groups, J. Funct. Anal. 129, 2 (1995), 268-292.