Representations of dynamical systems on Banach spaces not containing l₁

2008/03/15 by Eli Glasner, Michael Megrelishvili, Glasner, E. +1 · 2 citations
Mathematics · #37Bxx #46xx #54H15 #54H20 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0803.2320

openalex publication_date 2008/03/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For a topological group G, we show that a compact metric G-space is tame if and only if it can be linearly represented on a separable Banach space which does not contain an isomorphic copy of l₁ (we call such Banach spaces, Rosenthal spaces). With this goal in mind we study tame dynamical systems and their representations on Banach spaces.

Citations

• New algebras of functions on topological groups arising from G-spaces

Cited by

• Haar decompression and amenability of Ellis flows
• Circular orders: Topology and continuous actions

Related

• Banach representations and affine compactifications of dynamical systems
• Hereditarily non-sensitive dynamical systems and linear representations
• Tame functionals on Banach algebras
• Tameness and Rosenthal type locally convex spaces
• Eventual nonsensitivity and tame dynamical systems