关于随机共轭空间的各种定义及随机线性泛函各种有界性的某些评论(英文)  

Some Reviews on Various Definitions of a Random Conjugate Space together with Various Kinds of Boundedness of a Random Linear Functional

作　　者：郭铁信[1] 马瑞萍[1] 

机构地区：[1]厦门大学数学系,福建厦门361005

出　　处：《应用泛函分析学报》2004年第1期16-38,共23页Acta Analysis Functionalis Applicata

基　　金：Supported by the National Natural Science Foundation of China (1 0 0 71 0 63 );the Founda-tion for University Key Teachers by the Ministry of Education of China

摘　　要：　中心目的是详细廉政论在随机共轭空间理论形成过程中所经历的三个阶段的工作,尤其指出了这三个阶段工作之间的联系及本质差别;给出了强有界、拓扑有界及几乎处处有界随机线性泛函之间的关系;亦指出了在概率赋范空间上线性算子理论研究中目前存在的不足.A detailed review on the three stages of work in the formative course of the theory of random conjugate spaces is given, in particular the connections and essential distinctions among the three stages of work are pointed out while the relationships among strongly bounded, topologically bounded and almost surely bounded random linear functionals are also given. Finally some shortages currently available in the study of linear operators defined on probabilistic normed spaces are also pointed out.

关 键 词：随机共轭空间 随机线性泛函 概率赋范空间 E-范空间 

分 类 号：O177.39[理学—数学]