The extreme points of the unit ball of certain spaces of operators

In this note we discuss the set of extreme points of the unit ball of certain spaces of mappings. We prove that a mapping $T:E\to F'$ is an extreme point of the unit ball of the space $I(E,F')$ of integral mappings, if and only if it has the form $Tx=\langle x,a_0\rangle b_0$, where $a_0\in\operatorname{ext}S(E')$, $b_0\in\operatorname{ext}S(F')$