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

Published online by Cambridge University Press:  24 October 2008

C. M. Edwards  and
G. T. Rüttimann
C. M. Edwards
Affiliation:
The Queen's College, Oxford 0X1 4AW
G. T. Rüttimann
Affiliation:
Universität Bern, CH-3012 Bern, Switzerland
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Extract

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 in its dual space V* which forms a unital GM-space or a complete order unit space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 2 , September 1985 , pp. 305 - 322
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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