The Structure of C *-Convex Sets
The Structure of C *-Convex Sets
复制标题
C*-凸集的结构
DOI：
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发表时间：
1994
期刊：
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通讯作者：
P. B. Morenz
中科院分区：
文献类型：
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作者：
P. B. Morenz
Mn的紧C *-凸子集恰好对应于算子的n阶矩阵值域.本文的主要结果是发现线性极值点的“右”模拟，称为结构元，然后证明Mn的C *-凸子集的广义Krein-Milman定理。结构元素之间的关系和早期尝试的推广，称为C *-极值点，检查，解决肯定的猜想Loebl和保尔森[8]。还给出了凸集Caratheodory定理的C * -凸版本的改进界。
Abstract Compact C *-convex subsets of M n correspond exactly to n-th matrix ranges of operators. The main result of this paper is to discover the “right” analog of linear extreme points, called structural elements, and then to prove a generalised Krein-Milman theorem for C *-convex subsets of M n. The relationship between structural elements and an earlier attempted generalisation, called C *-extreme points, is examined, solving affirmatively a conjecture of Loebl and Paulsen [8]. An improved bound for a C * -convex version of the Caratheodory theorem for convex sets is also given.