Representations of dynamical systems on Banach spaces not containing 𝑙₁

Glasner, E.; Megrelishvili, M.

doi:10.1090/S0002-9947-2012-05549-8

Representations of dynamical systems on Banach spaces not containing $l_1$
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Trans. Amer. Math. Soc. 364 (2012), 6395-6424 Request permission

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 $l_1$ (we call such Banach spaces, Rosenthal spaces). With this goal in mind we study tame dynamical systems and their representations on Banach spaces.

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