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. 
@article{ASENS_1999_4_32_6_743_0,
     author = {Popa, Sorin},
     title = {The relative {Dixmier} property for inclusions of von {Neumann} algebras of finite index},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {743--767},
     publisher = {Elsevier},
     volume = {Ser. 4, 32},
     number = {6},
     year = {1999},
     doi = {10.1016/s0012-9593(00)87717-4},
     zbl = {0966.46036},
     mrnumber = {1717575},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(00)87717-4/}
}
TY  - JOUR
AU  - Popa, Sorin
TI  - The relative Dixmier property for inclusions of von Neumann algebras of finite index
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1999
SP  - 743
EP  - 767
VL  - 32
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/s0012-9593(00)87717-4/
DO  - 10.1016/s0012-9593(00)87717-4
LA  - en
ID  - ASENS_1999_4_32_6_743_0
ER  - 
%0 Journal Article
%A Popa, Sorin
%T The relative Dixmier property for inclusions of von Neumann algebras of finite index
%J Annales scientifiques de l'École Normale Supérieure
%D 1999
%P 743-767
%V 32
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/s0012-9593(00)87717-4/
%R 10.1016/s0012-9593(00)87717-4
%G en
%F ASENS_1999_4_32_6_743_0
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://www.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. | Numdam | 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

Cité par Sources :