Definition 0.1. A
representation of a Cc(G) topological ∗–algebra is defined as a continuous ∗–morphism from
Cc(G) to B(), where G is a topological groupoid, (usually a locally compact groupoid, Glc), is
a Hilbert spacehttps://physicslibrary.org/encyclopedia/NormInducedByInnerProduct.html,
and B() is the C∗-algebra of bounded linear operators on the Hilbert space ; of course, one
considers the inductive limit (strong) topology to be defined on Cc(G), and then also an
operator weak topology to be defined on B().
