On the facial structure of the unit balls in a GL-space and its dual

Edwards, C. M.; Rüttimann, G. T. (1985). On the facial structure of the unit balls in a GL-space and its dual. Mathematical proceedings of the Cambridge Philosophical Society, 98(2), pp. 305-322. Cambridge University Press 10.1017/S0305004100063489

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In the early sixties Effros[9] and Prosser[14] studied, in independent work, the duality of the faces of the positive cones in a von Neumann algebra and its predual space. In an implicit way, this work was generalized to certain ordered Banach spaces in papers of Alfsen and Shultz [3] in the seventies, the duality being given in terms of faces of the base of the cone in a base norm space and the faces of the positive cone of the dual space. The present paper is concerned with the facial structure of the unit balls in an ordered Banach space and its dual as well as the duality that reigns between these structures. Specifically, the main results concern the sets of norm-exposed and norm-semi-exposed faces of the unit ball V1 in a GL-space or complete base norm space V and the sets of weak*-exposed and weak*-semi-exposed faces of the unit ball V1* in its dual space V* which forms a unital GM-space or a complete order unit space.

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