Geodesic
Group C*-Algebras without the Completely Bounded Approximation Property
Uffe Haagerup1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
1Dept. of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
2It is proved that:
3(1) The Fourier algebra A(G) of a simple Lie group G of real rank at least 2 with finite center does not have a multiplier bounded approximate unit.
4(2) The reduced C*-algebra C
5*(Γ) of any lattice Γ in a non-compact simple Lie group of real rank at least 2 with finite center does not have the completely bounded approximation property.
6Hence, the results obtained by J. de Cannière and the author [
7, Amer. J. Math. 107 (1985) 455--500] for SO
8(n,1), n ≥ 2, and by M. Cowling [
9, in: Topics in modern harmonic analysis, Vol. I, II (Turin/Milan, 1982), Ist. Naz. Alta Mat. Francesco Severi, Rome (1983) 81--123] for SU(n,1) do not generalize to simple Lie groups of real rank at least 2.
10Keywords: Completely bounded approximation property, Group C*-algebras, weak amenability, lattices in Lie groups.
11MSC: 43A22, 43A80, 22E40, 22D25, 22D15
12[
Journal of Lie Theory, Tome 26 (2016) no. 3, pp. 861-887 
Uffe Haagerup. Group C*-Algebras without the Completely Bounded Approximation Property. Journal of Lie Theory, Tome 26 (2016) no. 3, pp. 861-887. http://geodesic.mathdoc.fr/item/JOLT_2016_26_3_a14/
@article{JOLT_2016_26_3_a14,
     author = {Uffe Haagerup},
     title = {Group {C*-Algebras} without the {Completely} {Bounded} {Approximation} {Property}},
     journal = {Journal of Lie Theory},
     pages = {861--887},
     year = {2016},
     volume = {26},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_3_a14/}
}
TY  - JOUR
AU  - Uffe Haagerup
TI  - Group C*-Algebras without the Completely Bounded Approximation Property
JO  - Journal of Lie Theory
PY  - 2016
SP  - 861
EP  - 887
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JOLT_2016_26_3_a14/
ID  - JOLT_2016_26_3_a14
ER  - 
%0 Journal Article
%A Uffe Haagerup
%T Group C*-Algebras without the Completely Bounded Approximation Property
%J Journal of Lie Theory
%D 2016
%P 861-887
%V 26
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2016_26_3_a14/
%F JOLT_2016_26_3_a14

Voir la notice de l'article provenant de la source Heldermann Verlag

It is proved that: