Edwards, C. M.; Rüttimann, G. T. (1985). On the facial structure of the unit balls in a GLspace and its dual. Mathematical proceedings of the Cambridge Philosophical Society, 98(2), pp. 305322. 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 normexposed and normsemiexposed faces of the unit ball V1 in a GLspace or complete base norm space V and the sets of weak*exposed and weak*semiexposed faces of the unit ball V1* in its dual space V* which forms a unital GMspace or a complete order unit space.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 
ISSN: 
03050041 
Publisher: 
Cambridge University Press 
Language: 
English 
Submitter: 
Marceline Brodmann 
Date Deposited: 
21 Jul 2020 12:13 
Last Modified: 
25 Jul 2020 04:50 
Publisher DOI: 
10.1017/S0305004100063489 
BORIS DOI: 
10.7892/boris.115457 
URI: 
https://boris.unibe.ch/id/eprint/115457 