概率赋准范空间中的算子讨论

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 pr obabilistic 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 probabilistie quasi-bounded operator in PQN space,conversely,it will not be true.