## The Second Duals of Beurling Algebras (Google eBook) |

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### Contents

1 | |

Definitions and Preliminary Results | 7 |

Repeated Limit Conditions | 25 |

Examples | 35 |

Introverted Subspaces | 45 |

Banach Algebras of Operators | 53 |

Beurling Algebras | 65 |

The Second Dual of l1Gω | 95 |

Algebras on Discrete Abelian Groups | 111 |

Beurling Algebras on F2 | 131 |

Topological Centres of Duals of Introverted Subspaces | 141 |

The Second Dual of L1Gω | 153 |

Derivations into Second Duals | 167 |

Open Questions | 175 |

### Common terms and phrases

2-weakly amenable abelian group American Math AP(G Arens regular Banach space Beurling algebra bounded approximate identity C*-algebra CB(G Chapter closed ideal closed subalgebra commutative continuous function Corollary define DEFINITION denoted diagonally bounded dual space element example exists function on G group algebra group G hence invariant isomorphic left-invariant Lemma Let G Let u j Let usbe lim inf lim lim limQ linear linear involution linear subspace Ll(G Ll(G,uj locally compact group locally compact space LUC(G mixed identity nilpotent predual PROOF Proposition repeated limits s e G second dual semigroup semisimple sequence strongly Arens irregular subadditive suppose t e G Theorem topological centres usbe a weight von Neumann algebra WAP(A WAP(G weakly compact weight function Аш Вш