## Abstract

In the present note we introduce tame functionals on Banach algebras. A functional f € A∗ on a Banach algebraA is tame if the naturally defined linear operator A → A∗, a Ü→ f Aa factors through Rosenthal Banach spaces (i.e., not containing a copy of l1). Replacing Rosenthal by reflexive we get a well known concept of weakly almost periodic functionals. So, always WAP(A) Tame(A). We show that tame functionals on the group algebra l11(G) are induced exactly by tame functions (in the sense of topological dynamics) on G for every discrete group G. That is, Tame(l11(G)) = Tame(G). Many interesting tame functions on groups come from dynamical systems theory. Recall that WAP(L1(G)) = WAP(G) (Lau [19], Ülger [28]) for every locally compact group G. It is an open question if Tame(L1(G)) = Tame(G) holds for (nondiscrete) locally compact groups.

Original language | English |
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Title of host publication | Banach Algebras and Applications - Proceedings of the International Conference |

Editors | Mahmoud Filali |

Publisher | Walter de Gruyter GmbH |

Pages | 213-226 |

Number of pages | 14 |

ISBN (Electronic) | 9783110601329 |

DOIs | |

State | Published - 26 Oct 2020 |

Event | 2017 23rd Conference on Banach Algebras and Applications - Oulu, Finland Duration: 3 Jul 2017 → 11 Jul 2017 |

### Publication series

Name | De Gruyter Proceedings in Mathematics |
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ISSN (Print) | 2942-4801 |

ISSN (Electronic) | 2942-4828 |

### Conference

Conference | 2017 23rd Conference on Banach Algebras and Applications |
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Country/Territory | Finland |

City | Oulu |

Period | 3/07/17 → 11/07/17 |

### Bibliographical note

Publisher Copyright:© 2020 Walter de Gruyter GmbH, Berlin/Munich/Boston.

## Keywords

- Asplund space
- Banach algebra
- Fragmentability
- Group algebra
- Reflexive space
- Rosenthal dichotomy
- Rosenthal space
- Tame functional
- WAP functional