Z-P-S空间中的若干概率分析问题

SOME PROBLEMS OF PROBABILISTIC ANALYSIS IN THE Z-P-S SPACE

基于Menger概率线性赋范空间,提出了Z-P-S空间这一新概念,研究了Z-P-S空间(E,F,△)中算子A的固有值与固有元问题,建立了紧连续算子A具有大于1的固有值λ且在■D上存在对应于λ的固有元的四个充分条件．

In this paper, a new concept of the Z-P-S space is introduced, based on Menger probabilistic linear normed space. Some problems of the intrinsic value and the intrinsic element of operator A are investigated in the Z-P-S space（E, F, △）. Four sufficient conditions for which the compact continuous operator A has an intrinsic value λ which is larger than 1 and has an intrinsic element corresponding with λ on ЭD are established.