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Gelfand-type theorems for dynamical Banach modules
Mathematische Zeitschrift ( IF 1.0 ) Pub Date : 2020-08-08 , DOI: 10.1007/s00209-020-02560-2
Henrik Kreidler , Sita Siewert

The representation theorems of Gelfand and Kakutani for commutative C*-algebras and AM- and AL-spaces are the basis for the Koopman linearization of topological and measure-preserving dynamical systems. In this article we prove versions of these results for dynamics on topological and measurable Banach bundles and the corresponding weighted Koopman representations on Banach modules.

中文翻译:

动力学 Banach 模的 Gelfand 型定理

Gelfand 和 Kakutani 的可交换 C*-代数以及 AM-和 AL-空间的表示定理是拓扑和测量保持动力系统的 Koopman 线性化的基础。在本文中,我们证明了拓扑和可测量 Banach 丛上动力学的这些结果的版本,以及 Banach 模块上相应的加权 Koopman 表示。
更新日期:2020-08-08
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