An Extremal Property of the Bloch Space

This is the authors' abstract. We don't add key points for this paper.

The Bloch space 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 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.