# Gelfand-Naimark representation theorem

The Gelfand-Naimark representation theorem is as follows:

Theorem 1.1

Every ${C}^{\mathrm{*}}$-algebra is isometrically isomorphic to a norm closed *-subalgebra ${\mathrm{B}}_{n\mathit{}c}\mathit{}\mathrm{(}\mathrm{H}\mathrm{)}$ of an algebra $\mathrm{B}\mathit{}\mathrm{(}\mathrm{H}\mathrm{)}$ of bounded operators^{} on some Hilbert space^{} $\mathrm{H}$. In particular, every finite dimensional ${C}^{\mathrm{*}}$-algebra is isomorphic to a direct sum of matrix algebras.

Title | Gelfand-Naimark representation theorem |
---|---|

Canonical name | GelfandNaimarkRepresentationTheorem |

Date of creation | 2013-03-22 12:57:58 |

Last modified on | 2013-03-22 12:57:58 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 12 |

Author | PrimeFan (13766) |

Entry type | Theorem |

Classification | msc 46L05 |

Related topic | ProofOfGelfandNaimarkRepresentationTheorem |