随机赋范空间中算子随机范数与共鸣定理及应用  

The Random Norm of Operators and Principle of Uniform Boundedness and Applications in Random Structure Space

作　　者：苏永福[1] 李素红[1] 

机构地区：[1]天津工业大学理学院数学系,天津300160

出　　处：《应用泛函分析学报》2006年第2期184-192,共9页Acta Analysis Functionalis Applicata

基　　金：天津市学科建设基金(100580204)

摘　　要：基于概率论理论基础,给出了随机赋范空间中算子的随机范数定义,在此基础上,应用逆算子定理证明了随机赋范空间中算子族的共鸣定理,它以Banach空间中的共鸣定理为特例,是Banach空间中的共鸣定理的随机化形式,随机化的共鸣定理刻划了在随机赋范空间框架下随机变量族的一致有界性.随机赋范空间中的共鸣定理将可能成为随机泛函分析与概率论的新应用工具.The purpose of this paper is to give the definition of random norm of operatots in the random normed spaces, and to prove the random principle of uniform boundedness. The random principle of uniform boundedness will express the uniform boundedness of family of random variable in the structure of random normed spaces. The random principle of uniform bounde dness will be also to devoted to the possible of applications of random functional analysis and probability theory, as a new tool.

关 键 词：随机赋范空间 随机范数 共鸣定理 应用 

分 类 号：O177.3[理学—数学]