Separably injective $C_\sigma$-spaces
  We show that a (complex) $C_\sigma$-space is separably injective 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