# Riesz representation theorem

For every continuous linear functional^{} $f$ on a Hilbert space^{} $\mathscr{H}$, there is a unique $u\in \mathscr{H}$ such that $f(x)=\u27e8x,u\u27e9$ for all $x\in \mathscr{H}$.

Note: $\u27e8x,u\u27e9$ denotes the inner product^{} between $x$ and $u$.

Title | Riesz representation theorem^{} |
---|---|

Canonical name | RieszRepresentationTheorem |

Date of creation | 2013-03-22 14:09:43 |

Last modified on | 2013-03-22 14:09:43 |

Owner | azdbacks4234 (14155) |

Last modified by | azdbacks4234 (14155) |

Numerical id | 9 |

Author | azdbacks4234 (14155) |

Entry type | Theorem |

Classification | msc 46C99 |

Related topic | RieszFischerTheorem |