An Extremal Property of the Bloch Space

The Bloch space <!-- MATH $\mathcal{B}$ --> is the space of functions f analytic in the unit disc D such that <!-- MATH $|f'(z)|(1 - |z{|^2})$ --> is bounded. It is shown that <!-- MATH $\mathcal{B}$ --> 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.