ABSTRACT: We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation EF and the conjugate function E* of the entanglement function E(ρ)=S(TrAρ). We then consider the conjectured strong superadditivity of the entanglement of formation EF(ρ)≥EF(ρI)+EF(ρII), where ρI and ρII are the reductions of ρ to the different Hilbert space copies, and prove that it is equivalent with subadditivity of E*. Furthermore, we show that strong superadditivity would follow from multiplicativity of the maximal channel output purity for quantum filtering operations, when purity is measured by Schatten p-norms for p tending to 1.