unitary representation

Let G be a topological groupMathworldPlanetmath. A unitary representationMathworldPlanetmath of G is a pair (π,H) where H is a Hilbert spaceMathworldPlanetmath and π:GU(H) is a homomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath such that the mapping of G×HH that sends (g,v) to π(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