# Riesz’ Lemma

Let $E$ be a normed space, $S\subset E$ a closed proper vector subspace, and $$. Then there is ${x}_{\alpha}\in E\setminus S$ such that $\parallel {x}_{\alpha}\parallel =1$ and $\parallel s-{x}_{\alpha}\parallel >\alpha $ for every $s\in S$.

Title | Riesz’ Lemma |
---|---|

Canonical name | RieszLemma |

Date of creation | 2013-03-22 14:56:11 |

Last modified on | 2013-03-22 14:56:11 |

Owner | gumau (3545) |

Last modified by | gumau (3545) |

Numerical id | 6 |

Author | gumau (3545) |

Entry type | Theorem |

Classification | msc 15A03 |

Classification | msc 54E35 |