# classification of separable Hilbert spaces

Let ${H}_{1}$ and ${H}_{2}$ be infinite dimensional, separable Hilbert spaces. Then there is an isomorphism^{} $f:{H}_{1}\to {H}_{2}$ which is also an isometry.

In other words, ${H}_{1}$ and ${H}_{2}$ are identical as Hilbert spaces^{}.

Title | classification of separable Hilbert spaces |
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Canonical name | ClassificationOfSeparableHilbertSpaces |

Date of creation | 2013-03-22 12:19:12 |

Last modified on | 2013-03-22 12:19:12 |

Owner | Evandar (27) |

Last modified by | Evandar (27) |

Numerical id | 5 |

Author | Evandar (27) |

Entry type | Theorem |

Classification | msc 46C15 |

Related topic | ClassificationOfHilbertSpaces |