Definition 0.1
A
representation
of a
topological
-algebra is defined as a
continuous
-morphism from
to
, where
is a topological groupoid, (usually a locally compact groupoid,
),
is a Hilbert spacehttp://planetphysics.org/encyclopedia/NormInducedByInnerProduct.html, and

is the

-algebra of bounded linear
operators
on the Hilbert space

; of course, one considers the inductive limit (strong) topology to be defined on

,
and then also an
operator
weak topology to be defined on

.