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 ⊂ C (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.