Grothendieck's double limit criteria for weakly compact set

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I was reading about Arens regularity of normed algebras in Palmer's book. He talks about the Grothendieck's double limit criteria for relatively weak compact sets in $X^*$ . Can some one provide me a proof or a link to an English version of his paper "Criteres de compacite' dans les espaces fonctionnels ge'ne'raux" ?