  We prove that the Harish-Chandra--Schwartz space associated with a discrete
subgroup of a semisimple Lie group is a dense subalgebra of the reduced
$C^*$-algebra of the discrete subgroup. Then, we prove that for the reduced
$C^*$-norm is controlled by the norm of the Harish-Chandra--Schwartz space.
This inequality is weaker than property RD and holds for any discrete group
acting isometrically, properly on a Riemannian symmetric space.
