复随机内积模上一类算子的谱定理

Spectral Theorems of A Class of Operators Defined on Complex Random Inner Product Modules

本文给出复随机内积模上几乎处处有界线性算子谱的几个基本定理，这些定理不但为随机内积模上几乎处处有界线性算子的进一步讨论有基本重要性，而且也为Ｈｉｌｂｅｒｔ空间上连续随机算子的谱研究提供了一个新途径。

In this paper several basic spectral theorems for almost surely bounded linear operators on complex random inner product modules are given. The results of this paper not only have fundamental importance in the further study for almost surely bounded linear operators on complex random inner product modules but also provide a new approach to study the spectral theory of continuous random linear operators on Hilbert spaces.