概率赋准范空间中的算子讨论  

Discussion on random operator in probabilistic quasi-normed space

作　　者：徐旭华[1] 葛倩[2] 张开银[3] XU Xu-Hua GE Qian ZHANG Kai-yin(Department of Mathematics, Jinjiang College, Siehuan University, Chengdu 610207, China Basic Teaching Department, Jinjiang College, Sichuan University, Chengdu 610207, China School of Physics and E｜eetronie Engineering, Fuyang Normal University, Fuyang 236037, China)

机构地区：[1]四川大学锦江学院数学学院,四川成都610207 [2]四川大学锦江学院基础教学部,四川成都610207 [3]阜阳师范学院物理与电子工程学院,安徽阜阳236037

出　　处：《兰州理工大学学报》2017年第5期153-156,共4页Journal of Lanzhou University of Technology

基　　金：安徽省自然科学基金(1308085MA13)

摘　　要：运用概率度量的思想讨论PQN空间中的随机算子,给出PQN空间中概率拟线性算子和概率等度连续算子的概念,研究它们的特性.在一定条件下,证明了PQN空间中线性算子的收敛算子是概率拟线性算子;PQN空间中的概率等度连续算子是概率拟有界算子,反之,不成立.Random operator in PQN space is discussed on the base of the idea of probabilistic metric,the concepts of probabilistic quasi-linear operator and probabilistic equimagnitude continuous operator in PQN space are given out,and their characteristics are studied.It is proved under certain conditions that the converged operator of a linear operator in PQN space will be a probabilistic quasi-linear operator and the probabilistic equimagnitude continuous operator will be a probabilistic quasi-bounded operator in PQN space,conversely,it will not be true.

关 键 词：PQN空间 概率拟线性算子 概率等度连续算子 τ-收敛 

分 类 号：O177.3[理学—数学]