representation of a Ccā¢(š–¦) *- topological algebra


Definition 0.1.

A representation of a Ccā¢(G) (http://planetmath.org/C_cG) topological *ā€“algebraPlanetmathPlanetmath is defined as
a continuous *ā€“morphismMathworldPlanetmath from Ccā¢(G) to Bā¢(H), where G is a topological groupoidPlanetmathPlanetmathPlanetmathPlanetmath, (usually a locally compact groupoid, Glā¢c), H is a Hilbert spaceMathworldPlanetmath, and Bā¢(ā„‹) is the C*-algebra of bounded linear operators on the Hilbert space ā„‹; of course, one considers the inductive limit (strong) topology to be defined on Ccā¢(š–¦), and then also an operator weak topology to be defined on Bā¢(ā„‹).

Title representation of a Ccā¢(š–¦) *- topological algebra
Canonical name RepresentationOfACcmathsfGTopologicalAlgebra
Date of creation 2013-03-22 18:16:24
Last modified on 2013-03-22 18:16:24
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 21
Author bci1 (20947)
Entry type Definition
Classification msc 81-00
Classification msc 18D05
Classification msc 55N33
Classification msc 55N20
Classification msc 55P10
Classification msc 55U40
Synonym groupoidPlanetmathPlanetmathPlanetmath C*-algebra representations
Related topic C_cG
Related topic BoundedOperatorsOnAHilbertSpaceFormACAlgebra
Related topic GelfandNaimarkSegalConstruction
Defines representation of a topological *- algebra