流的可分割性和表示
Fragmentability and representations of flows
摘要：
我们的目标是研究半群作用的弱星连续表示到"好“的范畴（例如，自反和Asplund）巴拿赫空间。这种方法导致流类似物的Eberlein和Radon-Nikodym Eulta和一类新的功能（Asplund功能），其中密切相关的Asplund表示，并包括类的弱殆周期函数。我们证明了一个流是弱概周期的当且仅当它有足够多的自反表示。本文的主要技术工具之一是碎裂性的概念（实际上来自Namioka和Phelps），并广泛用于巴拿赫空间理论的拓扑方面。我们探讨的“广义等度连续性”的流的碎片。这种统一的方法使我们能够获得几个动态应用。推广和加强了Akin-Auslander-Berg，Shtern，Veech-Troallic-Auslander和Hansel-Troallic的一些结果.我们经常建立，线性G-行动，弱和强拓扑重合，不一定封闭，G-极小子集。例如，这种行为是“轨道Kadec”。
英文摘要：
Our aim is to study weak star continuous representations of semigroup actions into the duals of ``good'' (e.g., reflexive and Asplund) Banach spaces. This approach leads to flow analogs of Eberlein and Radon-Nikodym compacta and a new class of functions (Asplund functions) which intimately is connected with Asplund representations and includes the class of weakly almost periodic functions. We show that a flow is weakly almost periodic iff it admits sufficiently many reflexive representations. One of the main technical tools in this paper is the concept of fragmentability (which actually comes from Namioka and Phelps) and widespreadly used in topological aspects of Banach space theory. We explore fragmentability as ``a generalized equicontinuity'' of flows. This unified approach allows us to obtain several dynamical applications. We generalize and strengthen some results of Akin-Auslander-Berg, Shtern, Veech-Troallic-Auslander and Hansel-Troallic. We establish that frequently, for linear G-actions, weak and strong topologies coincide on, not necessarily closed, G-minimal subsets. For instance such actions are ``orbitwise Kadec``.
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