# representations of Banach *-algebras are continuous

Theorem - Let $\pi :\mathcal{A}\u27f6\mathcal{B}(H)$ be a representation (http://planetmath.org/BanachAlgebraRepresentation) of a Banach *-algebra $\mathcal{A}$ on a Hilbert space^{} $H$. Then $\pi $ is bounded (http://planetmath.org/BoundedOperator) and $\parallel \pi \parallel \le 1$.

Title | representations of Banach *-algebras are continuous^{} |
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Canonical name | RepresentationsOfBanachalgebrasAreContinuous |

Date of creation | 2013-03-22 17:27:41 |

Last modified on | 2013-03-22 17:27:41 |

Owner | asteroid (17536) |

Last modified by | asteroid (17536) |

Numerical id | 5 |

Author | asteroid (17536) |

Entry type | Theorem |

Classification | msc 46K10 |