PlanetPhysics/Representation of a CcG Topological Algebra

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A \htmladdnormallink{representation {http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of a Failed to parse (unknown function "\grp"): {\displaystyle C_c(\grp)}
 topological $*$--algebra} is defined as a continuous $*$--morphism from Failed to parse (unknown function "\grp"): {\displaystyle C_c(\grp)}
 to $B(\mathbb {H} )$, where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \grp}
 is a \htmladdnormallink{topological groupoid {http://planetphysics.us/encyclopedia/GroupoidHomomorphism2.html}, (usually a locally compact groupoid, Failed to parse (unknown function "\grp"): {\displaystyle \grp_{lc}}
), $\mathbb {H}$ is a \htmladdnormallink{Hilbert space}}{http://planetphysics.us/encyclopedia/NormInducedByInnerProduct.html}, and $B(\mathbb {H} )$ is the $C^{*}$-algebra of bounded linear operators on the Hilbert space $\mathbb {H}$; of course, one considers the inductive limit (strong) topology to be defined on Failed to parse (unknown function "\grp"): {\displaystyle C_c(\grp)}
,

and then also an operator weak topology to be defined on $B(\mathbb {H} )$.