论文标题
统一的包蛋白群，用于群体素的作用
Uniform enveloping semigroupoids for groupoid actions
论文作者
论文摘要
我们为拓扑动力系统的（伪）等距扩展建立了新的特征。对于此类扩展，我们还扩展了有关相对不变的度量和傅立叶分析的结果，这些结果以前仅在最小情况下才知道到包括所有及物系统在内的明显更大的类别。为了绕过通过Ellis Semigroup对等轴测扩展的经典方法最小化的依赖，我们表明拓扑动力学系统的扩展可以描述为群组素的动作，然后改编包裹的半群以构建统一的包裹式半摩托群以进行群体类似动作。这种方法允许处理非微小系统的更复杂的轨道结构。 我们研究了一般类固醇动作的统一包膜，并将结果转换回动力系统的扩展情况。特别是，我们表明，在适当的假设下，当且仅当统一包络的半群体实际上是紧凑的群体时，群体的作用是（伪）等距。我们还基于抽象的Peter-Weyl-type定理提供了操作者理论表征，用于在Banach捆绑包上的紧凑，及时分组的表示，这具有独立的兴趣。
We establish new characterizations for (pseudo)isometric extensions of topological dynamical systems. For such extensions, we also extend results about relatively invariant measures and Fourier analysis that were previously only known in the minimal case to a significantly larger class, including all transitive systems. To bypass the reliance on minimality of the classical approaches to isometric extensions via the Ellis semigroup, we show that extensions of topological dynamical systems can be described as groupoid actions and then adapt the concept of enveloping semigroups to construct a uniform enveloping semigroupoid for groupoid actions. This approach allows to deal with the more complex orbit structures of nonminimal systems. We study uniform enveloping semigroupoids of general groupoid actions and translate the results back to the special case of extensions of dynamical systems. In particular, we show that, under appropriate assumptions, a groupoid action is (pseudo)isometric if and only if the uniform enveloping semigroupoid is actually a compact groupoid. We also provide an operator theoretic characterization based on an abstract Peter-Weyl-type theorem for representations of compact, transitive groupoids on Banach bundles which is of independent interest.
