摘要
概率赋范空间(简写为 PN 空间)中线性算子的研究已有很多结果.最近游兆永等人进一步完成了 PN 空间的等距度量化工作.本文在前述工作的基础上,系统地证明了 PN 空间中连续线性算子的一致有界性原理.特别是,本文的若干结论推广和改进了已有文献的相应结论.
Rcccntly,probabilistic norms of continuous lincar opcrators on locally boundcd PN
spaces were given in the paper[3],and the isometric mctrization of PN spaces was perfected
in paper[1]
The aim of the present paper is to study the uniformly bounded principle on PN
spaces.First,the authors use[3]to give the uniformly bounded principle on locally bound-
cd PN spaces and its application to random operators.Then,the authors utilizc[1]to ob-
tain the uniformly bounded principle on PN spaces,in particular,on random lincar normed
spaces.The results in the paper improve and generalizc the corresponding results in[1,4].
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
1990年第1期65-70,共6页
Journal of Xi'an Jiaotong University
关键词
概率赋范空间
线性算子
共鸣定理
linearoperator
probabilistic normed linearspaces
resonance therem
