An extremal property of the Bloch space

Abstract:

The Bloch space $\mathcal {B}$ is the space of functions f analytic in the unit disc D such that $|f’(z)|(1 - |z{|^2})$ is bounded. It is shown that $\mathcal {B}$ is the largest Möbius-invariant linear space of analytic functions that can be equipped with a Möbius-invariant seminorm in such a way that there is at least one “decent” continuous linear functional on the space. The term “decent” has a simple and precise definition.