  We show that the amenability of a locally compact group $G$ is equivalent to
a factorization property of $VN(G)$ which is given by $ VN(G) =
<VN(G)^*VN(G)>$. This answer partially two problems proposed by Z. Hu and M.
Neufang in their article \textit{Distinguishing properties of Arens
irregularity}, Proc. Amer. Math. Soc. 137 (2009), no. 5, 1753-1761.
