Extremal properties of the unit ball in \(H^ 1\) (Q1190267)

The authors prove the following main theorem: Theorem 1. Let \(f\in S(H^ 1)\) be outer. If \(d(\arg f,C(T)+H^ \infty)<{\pi\over 2}\), then \(f\) is an exposed point. Theorem 2. If \(f\) is an exposed point of \(B(H^ 1)\) and \(d(f/| f|,C(T)+H^ \infty)<1\) then \(f\) is a strongly exposed point.