Let be either the reduced or the maximal -algebra associated to a foliated manifold , and let be the elementary -algebra of compact operators. Then, it dim, it is shown that is isomorphic to the tensor product .
Soit la -algèbre, ou bien réduite ou bien maximale, associée à la variété feuilletée , et la -algèbre élémentaire des opérateurs compacts. Alors, si dim, on montre que est isomorphe à .
@article{AIF_1983__33_3_201_0, author = {Hilsum, Michel and Skandalis, Georges}, title = {Stabilit\'e des $C^*$-alg\`ebres de feuilletages}, journal = {Annales de l'Institut Fourier}, pages = {201--208}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {33}, number = {3}, year = {1983}, doi = {10.5802/aif.936}, mrnumber = {85f:58115}, zbl = {0505.46043}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.936/} }
TY - JOUR AU - Hilsum, Michel AU - Skandalis, Georges TI - Stabilité des $C^*$-algèbres de feuilletages JO - Annales de l'Institut Fourier PY - 1983 SP - 201 EP - 208 VL - 33 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.936/ DO - 10.5802/aif.936 LA - fr ID - AIF_1983__33_3_201_0 ER -
%0 Journal Article %A Hilsum, Michel %A Skandalis, Georges %T Stabilité des $C^*$-algèbres de feuilletages %J Annales de l'Institut Fourier %D 1983 %P 201-208 %V 33 %N 3 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.936/ %R 10.5802/aif.936 %G fr %F AIF_1983__33_3_201_0
Hilsum, Michel; Skandalis, Georges. Stabilité des $C^*$-algèbres de feuilletages. Annales de l'Institut Fourier, Volume 33 (1983) no. 3, pp. 201-208. doi : 10.5802/aif.936. http://archive.numdam.org/articles/10.5802/aif.936/
[1] Sur la théorie non commutative de l'intégration, Lect. Notes in Math., n° 725, Springer (1979), 19 à 143. | MR | Zbl
,[2] Survey of foliations and operator algebras, Operator algebras and applications, Proc. of Symp. in Pure Math., vol 38, part 1, A.M.S., Providence 1982. | Zbl
,[3] The longitudinal index theorem for foliations, Preprint I.H.E.S./M/82/24. | Zbl
, ,[4] Hilbert C*-modules, Theorems of Stinespring and Voiculescu, Journal of Operator Theory, vol. 4 n° 1 (1980). | MR | Zbl
,[5] Foliations with measure preserving holonomy, Ann. of Math., 102 (1975). | MR | Zbl
,[6] A groupoid approach to C*-algebras, Lect. Notes in Math., n° 793, Springer (1980). | MR | Zbl
,[7] Morita equivalence for C* and W* algebras, Journal of Pure and Applied Algebra, 5 (1974). | MR | Zbl
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