# Banach-Alaoglu theorem

Let $X$ be a normed space^{}, and let ${X}^{*}$ be its dual. Then the closed
unit ball of ${X}^{*}$,

$$\{f\in {X}^{*}:\parallel f\parallel \le 1\}$$ |

is compact^{} in the weak-$*$ topology^{}.

Title | Banach-Alaoglu theorem |
---|---|

Canonical name | BanachAlaogluTheorem |

Date of creation | 2013-03-22 14:48:44 |

Last modified on | 2013-03-22 14:48:44 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 6 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 46B10 |

Synonym | Alaoglu’s theorem |