## 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.

Original language | English |
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Pages (from-to) | 6395-6424 |

Number of pages | 30 |

Journal | Transactions of the American Mathematical Society |

Volume | 364 |

Issue number | 12 |

DOIs | |

State | Published - 2012 |

## Keywords

- Baire one function
- Banach representation of dynamical systems
- Enveloping semigroup
- Fragmentability
- Rosenthal's compact
- Rosenthal's dichotomy
- Tame system

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