representation of a $C_{c}(\mathsf{G})$ *- topological algebra

Definition 0.1.

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

 Title representation of a $C_{c}(\mathsf{G})$ *- 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