Characterization and properties of extreme operators into C(Y)

Let E be a real (or complex) Banach space, Y a compact Hausdorff space, and C(Y) the space of real (or complex) valued continuous functions on Y. If T is an extreme point in the unit ball of bounded linear operators from E into C(Y), then it is shown that T ^* maps (the natural imbedding in C(Y) ^* of)Y into the weak ^*-closure of ext S(E ^*), provided that Y is extremally disconnected, or E=C(X), where X is a dispersed compact Hausdorff space.