Nice Operators into G-Spaces

G -spaces are a class of L 1 -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 isomorphic to c 0 ( I ) for some set I . One of the main points in the proof is a characterization of spaces of type c 0 ( I ) by means of the structure topology on the extreme points of the dual space.