The Support Points of the Unit Ball in Bloch Space

Let H(D) be the topological vector space of all functions F holomorphic in the unit disc D. We consider the compact convex subset B̃1 = {F ∈ H(D) : F(0) = 0 ∧ |F′(z)| (1 − |z|2) ≤ 1 for z ∈ D} of H(D) and show that G ∈ B̃1 is a support point of B̃1 if and only if Λ(G) = {z ∈ D : |G′(z) (1 − |z|2) = 1} ≠ ∅. This is an application of a more general result which is concerned with the maximization of continuous linear functionals on a set K1 related to B̃1.