Vol. 52, No. 1, 1974

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Extreme operators on Choquet simplexes

Ka-Sing Lau

Vol. 52 (1974), No. 1, 129–142

If K is a Choquet simplex and X is a metrizable compact Hausdorff space, we let sK denote the set of extreme points of K with the facial topology and let S(L(C(X),A(K))) denote the set of continuous operators from C(X) into A(K) with norm not greater than 1. Our main purpose in this paper is to characterize the extreme points of S(L(C(X),A(K))). We show that T is an extreme point of S(L(C(X),A(K))) if and only if its adjoint τsends extreme points of K into X ∪−X C(X), also, the set of extreme points of S(L(C(X),A(K))) equals C(sK,X ∪−X).

Mathematical Subject Classification 2000
Primary: 46B10
Received: 10 February 1973
Published: 1 May 1974
Ka-Sing Lau