representation of a $C_c(\mathsf{G}) $ *- topological algebra
RepresentationOfAC_cG_dTopologicalAlgebra
2008-07-26 14:28:03
2008-09-18 20:42:51
Definition
representation of a topological *- algebra
representation of *-algebra on $B(\H)$
the $C^*$-algebra of bounded operators on the Hilbert space $\H$
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\begin{definition}
A \emph{representation of a \PMlinkname{$C_c(\grp)$}{C_cG} topological $*$--algebra} is defined as \\
a \emph{continuous $*$--morphism from $C_c(\grp)$ to $B(\H)$, where $\grp$ is a topological
groupoid, (usually a locally compact groupoid, $\grp_{lc}$), $\H $ is a Hilbert space},
and $B(\H)$ is the $C^*$-algebra of bounded linear operators on the Hilbert space $\H$;
of course, one considers the inductive limit (strong) topology to be defined on $C_c(\grp)$,
and then also an operator \emph{weak} topology to be defined on $B(\H)$.
\end{definition}