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Haagerup, Uffe

An example of a non nuclear C*-algebra, which has the metric approximation property. (English) Zbl 0408.46046

Invent. Math. 50, 279-293 (1979).
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Cited in 22 Reviews
Cited in 258 Documents

MSC:

46L10 General theory of von Neumann algebras
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
43A35 Positive definite functions on groups, semigroups, etc.

Keywords:

Nuclear C*-Algebra; Metric Approximation Property; Regular Representation of a Free Group; Convolution Operator; Approximative Unit

Citations:

Zbl 0397.46054; Zbl 0383.46011; Zbl 0262.43009
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Full Text: DOI EuDML

References:

[1] Akemann, C.A., Ostrand, P.A.: Computing norms in groupC *-algebras. Amer. J. Math.98, 1015-1047 (1976) · Zbl 0342.22008 · doi:10.2307/2374039
[2] Berg, C., Forst, G.: Potential theory of locally compact abelian groups. Ergebnisse der Mathematik87. Berlin, Heidelberg, New York: Springer 1975 · Zbl 0308.31001
[3] Choi, M.-D., Effros, E.G.: NuclearC *-algebras and the approximation property. Amer. J. Math.100, 61-79 (1978) · Zbl 0397.46054 · doi:10.2307/2373876
[4] Connes, A.: Classification of injective factors. Ann. Math.104, 73-115 (1976) · Zbl 0343.46042 · doi:10.2307/1971057
[5] Effros, E.G., Lance, E.C.: Tensor products of operator algebras, Advances in Math.25, 1-34 (1977) · Zbl 0372.46064 · doi:10.1016/0001-8708(77)90085-8
[6] Eymard, P.: L’algèbre de fourier d’un groupe localment compact. Bull. Soc. Math. France92, 181-236 (1964) · Zbl 0169.46403
[7] Greenleaf, F.P.: Invariant means on topological groups. New York: Van Nostrand 1969 · Zbl 0174.19001
[8] Haagerup, U.: On the dual weights for crossed products of von Neumann algebras II. Math. Scand.43, 119-140 (1978) · Zbl 0405.46053
[9] Kirshberg, E.:C *-nuclearity implies CPAP. Math. Nachr.76, 203-212 (1977) · Zbl 0383.46011 · doi:10.1002/mana.19770760115
[10] Lance, E.C.: On nuclearC *-algebras. J. funct. analysis12, 157-176 (1973) · Zbl 0252.46065 · doi:10.1016/0022-1236(73)90021-9
[11] Leinart, M.: Faltungsoperatoren auf gewissen diskreten Gruppen. Studia Math.12, 149-158 (1974) · Zbl 0262.43009
[12] Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces I, Ergebnisse der Mathematik92. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0362.46013
[13] Powers, R.T.: Simplicity of theC *-algebra associated with the free group on two generators. Duke Math. J.1, 151-156 (1975) · Zbl 0342.46046 · doi:10.1215/S0012-7094-75-04213-1
[14] Sakai, S.:C *-algebras andW *-algebras, Ergebnisse der Mathematik60. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0219.46042
[15] Szankowski, A.: paper in preparation.
[16] Takesaki, M.: On the cross norm of the direct product ofC *-algebras. Tohoku Math. J.16, 111-122 (1964) · Zbl 0127.07302 · doi:10.2748/tmj/1178243737
[17] Wassermann, S.: On Tensor products of certain groupC *-algebras. J. funct. analysis23, 239-254 (1976) · Zbl 0358.46040 · doi:10.1016/0022-1236(76)90050-1
[18] Wassermann, S.: InjectiveW *-algebras, Math. Proc. Camb. Phil. Soc.82, 39-47 (1977) · Zbl 0372.46065 · doi:10.1017/S0305004100053664
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