The Support Points of the Unit Ball in Bloch Space

Abstract

Let H(D) be the topological vector space of all functions F holomorphic in the unit disc D. We consider the compact convex subset 1 = {F [set membership, variant] H(D) : F(0) = 0 [logical and] |F'(z)| (1 - |z|2) z [set membership, variant] D} of H(D) and show that G [set membership, variant] 1 is a support point of 1 if and only if [Lambda](G) = {z [set membership, variant] D : |G'(z) (1 - |z|2) = 1} [not equal to] [empty set]. This is an application of a more general result which is concerned with the maximization of continuous linear functionals on a set 1 related to 1.