Abstract
G-spaces are a class of L1-preduals introduced by Grothendieck. We prove that if every extreme operator from any Banach space into a G-space, X, is a nice operator (that is, its adjoint preserves extreme points), then X is isometrically isomor- phic to c0(I ) for some set I. One of the main points in the proof is a characterization of spaces of type c0(I ) by means of the structure topology on the extreme points of the dual space.
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