On the classification of full factors of type III

Transactions of the American Mathematical Society

Volumn 356, Issue 10, 2004, Pages 4143-4159

  Shlyakhtenko, Dimitri ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644224013     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-04-03457-9     Document Type: Article

References (22)

1. L. Barnett, Free products of von Neumann algebras of type III, Proc. Amer. Math. Soc. 123 (1995), 543-553. MR 95c:46096
2. A. Connes, Correspondences, unpublished notes.
3. _, Une classification des facteurs de type III, Ann. scient. Éc. Norm. Sup. 6 (1973), 133-252. MR 49:5865
4. 1, J. Funct. Anal. 16 (1974), 415-455. MR 50:10840
5. _, Noncommutative geometry, Academic Press, 1994.
6. K. Dykema, Free products of finité dimensional and other von Neumann algebras with respect to non-tracial states, Free Probability (D.-V. Voiculescu, ed.), Fields Institute Communications, vol. 12, American Mathematical Society, 1997, pp. 41-88. MR 98c:46131
7. K. Dykema and F. Rǎdulescu, Compressions of free products of von Neumann algebras, Math. Ann. 316 (2000), no. 1, 61-82. MR 2001f:46100
8. C. C. Graham and O. C. McGehee, Essays in commutative harmonic analysis, Springer-Verlag, New York, 1979. MR 81d:43001
9. U. Haagerup, The standard form of von Neumann algebras, Math. Scand. 37 (1975), 271-283. MR 53:11387
10. E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vol. I, second ed., Springer-Verlag, Berlin, 1979, Structure of topological groups, integration theory, group representations. MR 81k:43001
11. S. Popa, Correspondences, INCREST preprint, 1986.
12. ∞) in subfactor theory, MSRI preprint 2000-032, to appear in Acta Math.
13. ∞) ⊗B(ℋ) scaling the trace, C.R. Acad. Sci. Paris 314 (1992), no. 1, 1027-1032. MR 93i:46111
14. λ factor with core isomorphic to the von Neumann algebra of a free group, tensor B(H), Recent advances in operator algebras (Orléans, 1992), no. 232, Astérisque, 1995, pp. 203-209. MR 97a:46083
15. D. Shlyakhtenko, Free quasi-free states, Pacific J. Math 177 (1997), 329-368. MR 98b:46086
16. _, Some applications of freeness with amalgamation, J. reine angew. Math. 500 (1998), 191-212. MR 99j:46079
17. _, A-valued semicircular systems, J. Func. Anal 166 (1999), 1-47. MR 2000j:46124
18. _, Microstates free entropy and cost of equivalence relations, Duke Math. J. 118 (2003), 375-425.
19. D.-V. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory II, Invent. Math. 118 (1994), 411-440. MR 96a:46117
20. _, The analogues of entropy and of Fisher's information measure in free probability theory, III, Geometric and Functional Analysis 6 (1996), 172-199. MR 96m:46119
21. _, A strengthened asymptotic freeness result for random matrices with applications to free entropy, IMRN 1 (1998), 41-64. MR 2000:46080
22. D.-V. Voiculescu, K. Dykema, and A. Nica, Free random variables, CRM monograph series, vol. 1, American Mathematical Society, 1992. MR 94c:46133