关于C(Ω)上有界线性算子表示测度的注记

Notes on Representing Measures of Bounded Linear Operators on C(Ω)

我们证明了紧Hausdorff空间Ω上的正则可数可加向量测度是C(Ω)上某一弱紧线性算子的表示测度,基于此和CΩ)上有界线性算子的理论讨论了Ω上可数可加向量测度和正则可数可加向量测度得到一些有趣的结果,特别地我们给出了RNP的一个新特征。

We prove that a regularly countably additive vector measure on a compact Hausdorff space Ω is the representing measure of a weakly compact linear operator on C(Ω). Making use of the preceding conclusion and some results about bounded linear operators on C(Ω), we discuss countably additive and regulaly countably additive vector measures and obtain some interesting results, in particular, we give a new characteristic of RNP.