Weak*-extreme points of injective tensor product spaces

Abstract

We investigate weak*-extreme points of the injective tensor product spaces of the form A ⊗ ∊ E, where A is a closed subspace of C (X) and E is a Banach space. We show that if x . X is a weak peak point of A then f (x) is a weak*-extreme point for any weak*-extreme point f in the unit ball of A⊗ ∊ E ⊂ (X,E). Consequently, when A is a function algebra, f (x) is a weak*-extreme point for all x in the Choquet boundary of A; the conclusion does not hold on the Silov boundary.