论文标题
halmos-von neumann定理，用于一般群体的作用
A Halmos-von Neumann theorem for actions of general groups
论文作者
论文摘要
我们为HALMOS-VON NEUMANN定理提供了一种新的分类方法，以实现一般拓扑组的行为。作为第一步，我们确定具有离散频谱的拓扑和衡量标准的不可还原系统的类别是等效的。这允许在拓扑动态框架中证明Halmos-Von Neumann定理。然后，我们使用Pontryagin和Tannaka-Krein二元理论来获得拓扑结构的分类结果，然后使用离散频谱进行测量提供的系统。作为副产品，我们获得了固定拓扑组的压缩的完整同构不变。
We give a new categorical approach to the Halmos-von Neumann theorem for actions of general topological groups. As a first step, we establish that the categories of topological and measure-preserving irreducible systems with discrete spectrum are equivalent. This allows to prove the Halmos-von Neumann theorem in the framework of topological dynamics. We then use the Pontryagin and Tannaka-Krein duality theories to obtain classification results for topological and then measure-preserving systems with discrete spectrum. As a byproduct, we obtain a complete isomorphism invariant for compactifications of a fixed topological group.
