no. 6
The relative Dixmier property for inclusions of von Neumann algebras of finite index
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 32 (1999) no. 6, pp. 743-767. 
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     title = {The relative {Dixmier} property for inclusions of von {Neumann} algebras of finite index},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
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     year = {1999},
     doi = {10.1016/s0012-9593(00)87717-4},
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Popa, Sorin. The relative Dixmier property for inclusions of von Neumann algebras of finite index. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 32 (1999) no. 6, pp. 743-767. doi : 10.1016/s0012-9593(00)87717-4. http://archive.numdam.org/articles/10.1016/s0012-9593(00)87717-4/

[Ak] Ch. Akemann, The dual space of an operator algebra, Trans. Amer. Math. Soc., Vol. 126, 1967, pp. 286-302. | MR | Zbl

[An] J. Anderson, Extensions, restrictions and representations of states on C*-algebras, Trans. Amer. Math. Soc., Vol. 249, 1979, pp. 303-329. | MR | Zbl

[ApZ] C. Apostol and L. Zsido, Ideals in W*-algebras and the function η of A. Brown and C. Pearcy, Revue Roumaine Math. Pures Appl., Vol. 18, 1973, pp. 1151-1170. | MR | Zbl

[BaDH] M. Baillet, Y. Denizeau and J.-F. Havet, Indice d'une espérance conditionnelle, Compositio Mathematica, Vol. 66, 1988, pp. 199-236. | Numdam | MR | Zbl

[BHKW] K. Berman, H. Halpern, V. Kaftal and G. Weiss, Matrix norm inequalities and the relative Dixmier property, Int. Eq. and Op. Th. J., Vol. 11, 1988, pp. 28-48. | MR | Zbl

[BoT] J. Bourgain and L. Tzafriri, On a problem of Kadison and Singer, J. Reine Angew. Math., Vol. 420, 1991, pp. 1-43. | MR | Zbl

[C1] A. Connes, Une classification des facteurs de type III, Ann. Sci. Ecole Norm. Sup., Vol. 6, 1973, pp. 133-252. | Numdam | MR | Zbl

[C2] A. Connes, Outer conjugacy classes of automorphisms of factors, Ann. Ecole Norm. Sup., Vol. 8, 1975, pp. 383-419. | Numdam | MR | Zbl

[C3] A. Connes, Compact metric spaces, Fredholm modules and hyperfiniteness, Ergod. Th. & Dynam. Sys., 1989, pp. 207-220. | MR | Zbl

[C4] A. Connes, Classification of injective factors, Ann. Math., Vol. 104, 1976, pp. 73-115. | MR | Zbl

[D1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris 1957, 1969. | Zbl

[D2] J. Dixmier, Quelques propriétés des suites centrales dans les facteurs de type II1, Invent. Math., Vol. 7, 1969, pp. 215-225. | MR | Zbl

[H] H. Halpern, Essential central spectrum and range for elements of a von Neumann algebra, Pacific J. Math., Vol. 43, 1972, pp. 349-380. | MR | Zbl

[ILPo] M. Izumi, R. Longo and S. Popa, A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras, J. Funct. Analysis, Vol. 155, 1998, pp. 25-63. | MR | Zbl

[J] V.F.R. Jones, Index for subfactors, Invent. Math., Vol. 72, 1983, pp. 1-25. | MR | Zbl

[KSi] R.V. Kadison and I.M. Singer, Extensions of pure states, Amer. J. Math., Vol. 81, 1959, pp. 383-400. | MR | Zbl

[MvN] F. Murray and J. Von Neumann, Rings of operators IV, Ann. of Math., Vol. 44, 1943, pp. 716-808. | MR | Zbl

[PiPo] M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Scient. Ec. Norm. Sup., Vol. 19, 1986, pp. 57-106. | Numdam | MR | Zbl

[P] F. Pop, Singular extensions of the trace and the relative Dixmier property in type II1 factors, preprint 1997.

[Po1] S. Popa, On a problem of R. V. Kadison on maximal abelian subalgebras, Invent. Math., Vol. 65, 1981, pp. 269-281. | MR | Zbl

[Po2] S. Popa, Classification of subfactors and their endomorphisms, CBMS Lecture Notes No 86, 1995. | MR | Zbl

[Po3] S. Popa, Free independent sequences in type II1 factors and related problems, Astérisque, Vol. 232, 1995, pp. 187-202. | MR | Zbl

[Po4] S. Popa, Classification of amenable subfactors of type II, Acta Math., Vol. 172, 1994, pp. 163-255. | MR | Zbl

[Po5] S. Popa, Some properties of the symmetric enveloping algebras of a subfactor with applications to amenability and property T, preprint 1997.

[Po6] S. Popa, Correspondences, INCREST preprint 1986.

[Po7] S. Popa, Maximal injective subalgebras in factors associated with free groups, Adv. in Math., Vol. 50, 1983, pp. 27-48. | MR | Zbl

[PoR] S. Popa and F. Radulescu, Derivations of von Neumann algebras into the compact ideal space of a semifinite algebra, Duke Math. J., Vol. 57, 1988, pp. 485-518. | MR | Zbl

[Re] G.A. Reid, On the Calkin representations, Proc. London Math. Soc., Vol. 23, 1971, pp. 547-564. | MR | Zbl

[Sa] S. Sakai, The theory of W*-algebras, Lecture Notes, Yale University, 1962.

[S] S. Stratila, Modular theory, Editura Academiei and Abacus Press, Bucharest and Tunbridge-Wells, 1981. | Zbl

[SZ1] S. Stratila and L. Zsido, An algebraic reduction theory for W* algebra, Rev. Roum. Math. Pures Appl., Vol. 18, 1973, pp. 403-460. | MR | Zbl

[SZ2] S. Stratila and L. Zsido, Lectures on von Neumann algebras, Editura Academiei and Abacus Press, Bucharest and Tunbridge-Wells, 1979. | MR | Zbl

[T] M. Takesaki, Conditional expectations in von Neumann algebras, J. Funct. Anal., Vol. 9, 1972, pp. 306-321. | MR | Zbl

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