representation of a $C_c(𝖦)$ *- topological algebra

Definition 0.1.

A representation of a $C_c\mathit{}\mathrm{(}\mathrm{G}\mathrm{)}$ (http://planetmath.org/C_cG) topological $\mathrm{*}$–algebra is defined as
a continuous $\mathrm{*}$–morphism from $C_c\mathit{}\mathrm{(}\mathrm{G}\mathrm{)}$ to $B\mathit{}\mathrm{(}\mathrm{H}\mathrm{)}$, where $\mathrm{G}$ is a topological groupoid, (usually a locally compact groupoid, ${\mathrm{G}}_{l\mathit{}c}$), $\mathrm{H}$ is a Hilbert space, and $B(\mathscr{H})$ is the $C^{*}$-algebra of bounded linear operators on the Hilbert space $\mathscr{H}$; of course, one considers the inductive limit (strong) topology to be defined on $C_c(𝖦)$, and then also an operator weak topology to be defined on $B(\mathscr{H})$.

Title	representation of a $C_c(𝖦)$ *- 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	groupoid C*-algebra representations
Related topic	C_cG
Related topic	BoundedOperatorsOnAHilbertSpaceFormACAlgebra
Related topic	GelfandNaimarkSegalConstruction
Defines	representation of a topological *- algebra