English

Group C*-algebras without the completely bounded approximation property

Operator Algebras 2016-03-02 v1

Abstract

It is proved that: (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. (2) The reduced C*-algebra of any lattice in a non-compact simple Lie group of real rank at least 2 with finite center does not have the completely bounded approximation property. Hence, the results obtained by J. de Canniere and the author for SO(n,1), n at least 2, and by M. Cowling for SU(n,1) do not generalize to simple Lie groups of real rank at least 2.

Keywords

Cite

@article{arxiv.1603.00209,
  title  = {Group C*-algebras without the completely bounded approximation property},
  author = {Uffe Haagerup},
  journal= {arXiv preprint arXiv:1603.00209},
  year   = {2016}
}

Comments

Typeset version of a handwritten manuscript from May 1986

R2 v1 2026-06-22T13:00:47.248Z