# quotients in ${C}^{*}$-algebras

Theorem - Let $\mathcal{A}$ be a ${C}^{*}$-algebra (http://planetmath.org/CAlgebra) and $\mathcal{I}\subseteq \mathcal{A}$ a closed (http://planetmath.org/ClosedSet) ideal. Then the involution (http://planetmath.org/InvolutaryRing) in $\mathcal{A}$ induces a well-defined involution in $\mathcal{A}/\mathcal{I}$ and $\mathcal{A}/\mathcal{I}$ is a ${C}^{*}$-algebra with this involution and the quotient norm.

Title | quotients in ${C}^{*}$-algebras |
---|---|

Canonical name | QuotientsInCalgebras |

Date of creation | 2013-03-22 17:41:39 |

Last modified on | 2013-03-22 17:41:39 |

Owner | asteroid (17536) |

Last modified by | asteroid (17536) |

Numerical id | 5 |

Author | asteroid (17536) |

Entry type | Theorem |

Classification | msc 46L05 |

Related topic | NuclearCAlgebra |