# unitary representation

Let $G$ be a topological group^{}. A *unitary representation ^{}* of $G$
is a pair $(\pi ,H)$ where $H$ is a Hilbert space

^{}and $\pi :G\to U(H)$ is a homomorphism

^{}such that the mapping of $G\times H\to H$ that sends $(g,v)$ to $\pi (g)v$ is continuous. Here $U(H)$ denotes the set of unitary operators of $H$. The group $G$ is said to act unitarily on $H$ or sometimes, $G$ is said to act by unitary representation on $H$.

Title | unitary representation |
---|---|

Canonical name | UnitaryRepresentation |

Date of creation | 2013-03-22 16:51:45 |

Last modified on | 2013-03-22 16:51:45 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 4 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 20C35 |

Related topic | IrreducibleUnitaryRepresentationsOfCompactGroupsAreFiniteDimensional |