\(K\)-amenability for \(\text{SU}(n,1)\) (Q1310807)

The original version of this important paper [see also the authors in Contemp. Math. 70, 103-111 (1988; Zbl 0662.46073)] has been circulating already for many years and was used by \textit{P. Julg} and \textit{G. Kasparov} [C. R. Acad. Sci., Paris, Sér. I 313, 259-264 (1991; Zbl 0752.19005)], to prove that \(\text{SU}(n,1)\) even satisfies the strong Connes-Kasparov conjecture. The \(K\)-amenability of \(\text{SU}(n,1)\) is shown, constructing a homotopy between the trivial Fredholm \(\text{SU}(n,1)\)-module and a Fredholm \(\text{SU}(n,1)\)-module for which the representations of \(\text{SU}(n,1)\) are weakly contained in the left regular representation.