Let $K(X, Y)$ be the collection of all compact linear operators from $X$ to $Y$ and $K(X, Y)^*$ be the dual of $K(X, Y)$. I am interested to know the extreme points of the unit ball of $K(X, Y)^*$. In the year 1977, Fakhouri proved that, for real spaces $$\operatorname{ext}(B(K(X, Y)^*))\subseteq \operatorname{ext}(B(X^{**}))\otimes \operatorname{ext}(B(Y^*)).$$ A generalization of this result was given by Collins and Ruess in 1983. Ruess and Stegall proved the converse inclusion for real case. I am struggling with the proof. I do not know the language written by Fakhouri. I could not able to get any English version of the work. Next, everybody cited Fakhouri's work for concluding the first inclusion. Therefore, I definitely need to understand Fakhouri's work. Please help me by explaining the proof in English version. Or, give any references where I can get the proof. Any kind of help is appreciated. Thank you in advance.
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