Invariant means on the isometry semigroups of C*-algebras and von Neumann algebras

Let A be a Von Neumann algebra with isometry semigroup I, give I the relative ultraweak topology. Then I is a topological semigroup. It is known that A is amenable if and only if there exists a right invariant mean on LUC(I). We prove that A is amenable if and only if there exists a right invariant mean on WLUC(I), we also show that if A is a unital C*-algebra with isometry semigroup S, A is amenable if and only if there exists a right invariant mean on LUC(S).