Abstract
In this article we study the embeddability of cones in a Banach space X. First we prove that c0 is embeddable in X if and only if its positive cone c + is embeddable in X and we study some properties of Banach spaces containing c0 in the light of this result. So, unlike with the positive cone of � 1 which is embeddable in any non-reflexive space, c + 0 has the same behavior as the whole space c0. In the second part of this article we give a characterization of Grothendieck spaces X according to the geometry of cones of X ∗ . By these results we give a partial positive answer to a
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