Indecomposable Positive Additive Functionals
Indecomposable Positive Additive Functionals
复制标题
不可分解正加性泛函
DOI：
10.1112/jlms/s1-41.1.318
复制
发表时间：
1966
影响因子：
1.2
通讯作者：
A. Hayes
中科院分区：
文献类型：
--
作者：
A. Hayes
设E是有向偏序线性空间。E上的一个正线性泛函被称为不可分解的，如果E上的每个正线性泛函< f>是（f）的标量倍。邦索尔[2]得到了当E有序单位时，这类泛函的核的特征，Kist [5]将其推广到任何有向偏序线性空间。这是一个很容易的结果，当E是格序的不可分解的正线性泛函正是那些线性泛函，保持格关系。工作报告在这里开始的想法，即使E是不格有序它可能仍然有可能将不可分解的正线性泛函作为那些积极的线性泛函（粗略地说）来尽可能接近的结构E允许保持晶格关系。事实证明是这样的（定理1的推论1中给出了一个精确的陈述）。一个新的表征方面的内核也给出了。
Let E be a directed partially ordered linear space. A positive linear functional, tf>, on E is called indecomposable if every positive linear functional, ijj, on E with 0^«/»^< f> is a scalar multiple of (f>. Bonsall [2] obtained a characterisation of such functionals, when E has an order unit, in terms of their kernels, and Kist [5] extended this to any directed partially ordered linear space. It is an easy consequence of this characterisation that when E is lattice ordered the indecomposable positive linear functionals are precisely those linear functionals which preserve the lattice relations. The work reported on here began with the idea that even if E is not lattice ordered it might nevertheless be possible to characterise the indecomposable positive linear functionals as those positive linear functionals which (roughly speaking) come as close as the structure of E permits to preserving lattice relations. This turns out to be the case (a precise statement is given in Corollary 1 to Theorem 1). A new characterisation in terms of kernels is also given.