Geodesic
Extreme points of the unit ball of the operator Hardy space $H^\infty(E\to E_*)$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 160-164 
S. R. Treil'. Extreme points of the unit ball of the operator Hardy space $H^\infty(E\to E_*)$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 160-164. http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a15/
@article{ZNSL_1986_149_a15,
     author = {S. R. Treil'},
     title = {Extreme points of the unit ball of the operator {Hardy} space $H^\infty(E\to E_*)$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {160--164},
     year = {1986},
     volume = {149},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a15/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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)$\inf\{\|(I-\theta\theta^*)^{1/2}(e+\sum_{k\geqslant1}\bar z^ke_k)\|:e_k\in E\}=0$, $\forall e\in E$.