Separably injective C*-algebras
  We show that a C*-algebra is a $1$-separably injective Banach space if, and only if, it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff space $\Omega$. 
Cho-Ho Chu and Lei Li
math.FA