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For a topological group G, we show that a compact metric G-space is tame ifand only if it can be linearly represented on a separable Banach space whichdoes 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 andtheir representations on Banach spaces.

Representations of dynamical systems on Banach spaces not containing $l_1$