Group C*-Algebras without the Completely Bounded Approximation Property

By Uffe Haagerup. Journal of Lie theory, 2016

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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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d363f159d3e85befd4832a190e03a02397cd0937

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In Algebra and Number Theory

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Citations in the corpus

• Tensor Products of C*-Algebras and Operator Spaces (2020, background): “Haagerup proved in 1986 (see [108]) that for a discrete group G, the λ-CBAP for C∗ λ(G) is equivalent to the weak* λ-CBAP for MG, and moreover when this holds we may always find the net (Ti) formed of finite rank multipliers (see Proposition 3.”