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