On the facial structure of the unit balls in a GL-space and its dual
On the facial structure of the unit balls in a GL-space and its dual
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GL空间中单位球的面结构及其对偶
DOI：
10.1017/s0305004100063489
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发表时间：
1985
影响因子：
0.8
通讯作者：
G. Rüttimann
中科院分区：
文献类型：
--
作者：
C. Edwards;G. Rüttimann
在60年代早期，Effros[9]和Prosser[14]在各自独立的工作中研究了von Neumann代数及其前偶空间中正锥面的对偶性。在70年代Alfsen和Shultz[3]的论文中，以隐式的方式将这一工作推广到某些有序的Banach空间中，对偶性是由基范数空间中锥的基底面的面和对偶空间中正锥的面给出的。本文研究了有序巴拿赫空间中单位球的面结构及其对偶，以及这些结构之间的对偶性。具体而言，主要结果涉及到单位球V1在gl -空间或完备基范数空间V中的范数暴露面和范数半暴露面的集合，以及单位球在其对偶空间V*中的弱*暴露面和弱*半暴露面的集合，该对偶空间V*构成了一元gm -空间或完备序单位空间。
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.