Extreme points of the unit ball of the operator Hardy space $H^\infty(E\to E_*)$

The following description of extreme points of the unit ball of the operator Hardy space $H^\infty(E\to E_*)$ is obtained.
Theorem. Let $\theta\in H^\infty(E\to E_*)$ and $\|\theta\|_\infty\leqslant1$. Then $\theta$ is an extreme point of the unit ball of $H^\infty(E\to E_*)$ if and only if at least one of two following conditions holds:
a)$\inf\{\|(I-\theta^*\theta)^{1/2}(e+\sum_{k\geqslant1}z^ke_k)\|:e_k\in E\}=0$, $\forall e\in E$;
b)$\inf\{\|(I-\theta\theta^*)^{1/2}(e+\sum_{k\geqslant1}\bar z^ke_k)\|:e_k\in E\}=0$, $\forall e\in E$.