Strongly exposed points in bases for the positive cone of ordered Banach spaces and characterizations of l1(Г)
Strongly exposed points in bases for the positive cone of ordered Banach spaces and characterizations of l1(Г)
复制标题
有序 Banach 空间的正锥基中的强暴露点和 l1(Г) 的表征
DOI：
10.1017/s0013091500017648
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发表时间：
1986
影响因子：
0.7
通讯作者：
I. Polyrakis
中科院分区：
文献类型：
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作者：
I. Polyrakis
关于Banach空间中闭、凸、有界集的极端、强暴露点的研究，特别是通过Radon-Nikodaim性质与Banach空间的闭、凸、有界子集的几何学的相互联系而得到了发展[5]，[2]。在序Banach空间理论以及Choquet理论中，[4]，我们感兴趣的是研究一种特殊类型的凸集，不一定是有界的，即正锥的基。在[7]中，研究了具有Radon-Nikodrom性质的Banach空间X的闭凸子集K的几何（端点，可凹性），特别强调了K是X的子锥P的基的情况。在[6，定理1]中，证明了一个无限维的可分的局部实格Banach空间与l1序同构当且仅当X具有Krein-Milman性质且其正锥有界基.
The study of extreme, strongly exposed points of closed, convex and bounded sets in Banach spaces has been developed especially by the interconnection of the Radon–Nikodým property with the geometry of closed, convex and bounded subsets of Banach spaces [5],[2] . In the theory of ordered Banach spaces as well as in the Choquet theory, [4], we are interested in the study of a special type of convex sets, not necessarily bounded, namely the bases for the positive cone. In [7] the geometry (extreme points, dentability) of closed and convex subsets K of a Banach space X with the Radon-Nikodým property is studied and special emphasis has been given to the case where K is a base for acone P of X. In [6, Theorem 1], it is proved that an infinite-dimensional, separable, locally solid lattice Banach space is order-isomorphic to l1 if, and only if, X has the Krein–Milman property and its positive cone has a bounded base.