Group C*-algebras without the completely bounded approximation property

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.

arXiv commentTypeset version of a handwritten manuscript from May 1986

References in corpus (1)

• Examples of groups which are not weakly amenable

Cited by in corpus (10)

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• On the structural theory of II_1 factors of negatively curved groups, II: Actions by product groups
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• The weak Haagerup property II: Examples
• Von Neumann equivalence and group exactness
• Decomposable Fourier Multipliers and an Operator-Algebraic Characterization of Amenability
• Weak amenability and simply connected Lie groups
• Approximation properties for $p$-adic symplectic groups and lattices
• Weak amenability of Lie groups made discrete