概率赋准范空间的随机算子和有界性分析  

Opera tor and Boundedness in Probabilistic Quasi-normed Space

作　　者：徐旭华[1] 葛倩[2] 李亮 王龙[4] XU Xu-hua;GE Qian;LI Liang;WANG Long(Department of Mathematics,Sichuan University Jinjiang College,Chengdu 610207,China;Basic Teaching Department,Sichuan University Jinjiang College,Chengdu 610207,China;School of Mechanics and Optoelectronics Physics,Anhui University of Science and Technology,Huainan 232001,China;School of Mechanical Engineering,Anhui University of Science and Technology,Huainan 232001,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]安徽理工大学力学与光电物理学院,安徽淮南232001 [4]安徽理工大学机械工程学院,安徽淮南232001

出　　处：《数学的实践与认识》2020年第16期205-210,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(51705002);安徽省自然科学基金(1708085QA17,1708085QE123)。

摘　　要：运用概率度量的概念讨论了PQN空间中的随机算子,同时研究了随机算子的有界性,如拓扑有界算子、(概率)拟有界算子、D-有界算子等.经研究得到:在一定条件下,两个拓扑有界的PQN空间之间的拓扑有界算子构成一个PQN空间,两个PQN空间之间的D-有界线性算子构成一个向量空间.Based on the concept of probabilistic metric,random operators in PQN space are researched in this work.Boundedness properties of operators such as probabilistic Quasibounded operator,t opologically bounded operator,D-bounded opera tor,and so on are discussed.Conclusions can be drawn from the analysis:(1)the set of all topologically bounded operators between two topologically bounded PQN spaces is also a PQN space;(2)the Set of D-bounded linear operator formed between two PQN spaces is a vector space under certain conditions.

关 键 词：PQN 算子 拓扑有界 (概率)拟有界 D-有界 

分 类 号：O177[理学—数学]