Almost-additive ergodic theorems for amenable groups

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• 作者：Felix Pogorzelski
• 关键词：Ergodic theorems ; Group dynamics ; Amenability ; Integrated density of states
• 刊名：Journal of Functional Analysis
• 出版年：2013
• 出版时间：15 October, 2013
• 年：2013
• 卷：265
• 期：8
• 页码：1615-1666
• 全文大小：480 K

文摘

In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By extending the theory of ¦Å-quasi tiling techniques, we set the ground for far-reaching applications in the theory of group dynamics. In particular, we verify the almost-everywhere convergence of abstract bounded, additive processes, as well as a Banach space approximation result for the spectral distribution function (integrated density of states) for random operators on discrete structures in a metric space. Further, we include a Banach space valued version of the Lindenstrauss ergodic theorem for amenable groups.