In this paper we prove that any operator which is given by convolution with a suitable distribution on a compact semisimple Lie group is of type $(\f{1}{2}, \f{1}{2}).$ Our main result is:
Theorem 1.1 If $K$ is an operator defined by convolution, so $Kf=k*f,$ then, for suitable distributions $k,$ the operator $K$ has the type $(\f{1}{2}, \f{1}{2}).$