论文标题
Hahn-Jordan的分解和Riesz-Frechet代表定理在Riesz空间中
A Hahn-Jordan decomposition and Riesz-Frechet representation theorem in Riesz spaces
论文作者
论文摘要
我们在瑞斯的空间中给出了一个霍恩 - 约旦分解，该空间概括了[{{{\ sc B. A. Watson}，{Andôdouglastype Type type Theore type type in Riesz s in Riesz spaces at liess the Riess} {\ em Postitivity} {\ em Postitivity，} $ t $ -strong Dual，其中$ t $是Riesz太空的条件期望运营商。沃森的结果是专门制定的，目的是协助证明Riesz空间有条件期望运算符具有给定范围空间的情况，即Andô-Douglas类型的结果。这是在Riesz空间中的马尔可夫过程和玛格尔理论的研究中需要的。在当前的工作中，我们的兴趣是Riesz-Frechet代表定理，为此，Hahn-Jordan分解的另一种变体。
We give a Hahn-Jordan decomposition in Riesz spaces which generalizes that of [{{\sc B. A. Watson}, {An Andô-Douglas type theorem in Riesz spaces with a conditional expectation,} {\em Positivity,} {\bf 13} (2009), 543 - 558}] and a Riesz-Frechet representation theorem for the $T$-strong dual, where $T$ is a Riesz space conditional expectation operator. The result of Watson was formulated specifically to assist in the proof of the existence of Riesz space conditional expectation operators with given range space, i.e., a result of Andô-Douglas type. This was needed in the study of Markov processes and martingale theory in Riesz spaces. In the current work, our interest is a Riesz-Frechet representation theorem, for which another variant of the Hahn-Jordan decomposition is required.
