The support points of the unit ball in Bloch space
Let \(H({\mathbf D})\) be the topological vector space of all functions \(F\) holomorphic in the unit disc \({\mathbf D}\). The author considers the compact convex subset \[ \widetilde{\mathcal B}_ 1= \{F\in H({\mathbf D}): F(0)= 0\land | F'(z)|(1- | z|^ 2)\leq 1\text{ for }z\in {\mathbf D}\} \] of \(H({\mathbf D})\) and shows that \(G\in \widetilde{\mathcal B}_ 1\) is a support point of \(\widetilde{\mathcal B}_ 1\) if and only if \[ \Lambda(G)= \{z\in {\mathbf D}: | G'(z)|(1-| z|^ 2)= 1\}\neq\emptyset. \] This is an application of a more general result which is concerned with the maximization of continuous linear functionals on a set \({\mathcal K}_ 1\) related to \(\widetilde{\mathcal B}_ 1\).
support points of the unit ball in Bloch space
maximization of continuous linear functionals
scientific article; zbMATH DE number 635903