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Weak amenability and semidirect products in simple Lie groups. (English) Zbl 0860.43005

Let \(G\) be a locally compact group. The author studies the invariant \(\Lambda(G)\) which is the infimum over all numbers \(C>0\) for which the Fourier algebra \(A(G)\) admits a \(C\)-completely bounded multiplier. His main result is: If \(G\) is a noncompact, simple, connected, real Lie group such that its Lie algebra has real rank \(\geq 2\), then \(\Lambda(G)=\infty\). This extends a result due to U. Haagerup [Injectivity and decomposition of completely bounded maps. Lect. Notes Math. 1132, 170-222 (1985; Zbl 0591.46050)] who had the extra assumption that the center of \(G\) should be finite.

MSC:

43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A80 Analysis on other specific Lie groups
46J10 Banach algebras of continuous functions, function algebras
22D99 Locally compact groups and their algebras

Citations:

Zbl 0591.46050
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References:

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