PlanetPhysics/Representation of a CcG Topological Algebra

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A \htmladdnormallink{representation {http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of a $C_c(\grp)$ topological $$*$$--algebra} is defined as a continuous $$*$$--morphism from $$C_c(\grp)$$ to $$B(\mathbb{H})$$, where $$\grp$$ is a \htmladdnormallink{topological groupoid {http://planetphysics.us/encyclopedia/GroupoidHomomorphism2.html}, (usually a locally compact groupoid, $$\grp_{lc}$$), $$\mathbb{H} $$ 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 $$C_c(\grp)$$, and then also an operator weak topology to be defined on $$B(\mathbb{H})$$.