# topologically irreducible representations are algebrically irreducible for ${C}^{*}$-algebras

Theorem - Every topologically irreducible representation^{} (http://planetmath.org/BanachAlgebraRepresentation) of a ${C}^{*}$-algebra^{} (http://planetmath.org/CAlgebra) is algebraically irreducible.

$Remark-$ It follows easily from the definition that algebraically irreducible of any Banach *-algebra are always topologically irreducible. The above theorem says that for ${C}^{*}$-algebras the converse is also true.

Title | topologically irreducible representations are algebrically irreducible for ${C}^{*}$-algebras |
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Canonical name | TopologicallyIrreducibleRepresentationsAreAlgebricallyIrreducibleForCalgebras |

Date of creation | 2013-03-22 17:27:47 |

Last modified on | 2013-03-22 17:27:47 |

Owner | asteroid (17536) |

Last modified by | asteroid (17536) |

Numerical id | 5 |

Author | asteroid (17536) |

Entry type | Theorem |

Classification | msc 46L05 |