Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one (Q1823419)

Let G be a locally compact group, A(G) the space of matrix coefficients of the regular representation. Then the dual of A(G) is the algebra VN(G) of bounded linear operators on \(L^ 2(G)\) commuting with right translations. Let \(M_ 0\) be the space of completely bounded multipliers of A(G) (i.e. the corresponding induced operator on VN(G) is completely bounded). For some G there exists a net \(m_ i\), \(i\in I\), such that \(m_ i\) tends to 1 uniformly on compacta and \(\| m_ i\|_{M_ 0}\leq L\). Let \(\Lambda_ G\) be the infimum of such L's. The authors calculate \(\Lambda_ G\) for all non-compact real-rank-one simple Lie groups with finite center.