  Given a separable unital C*algebra $C$, let $E_n$ denote the Hilbert module
equal to the completion of the Schwartz space of rapidly decreasing smooth
functions from $R^n$ to $C$ equipped with the $C$-valued inner product given by
integration. Let $B$ denote the space of all smooth functions with bounded
derivatives from $R^n$ to $C$. For each $a$ in $B$, let $O(a)$ denote the
pseudodifferential operator of symbol $a$. $O$ maps $B$ to $H$, the set of all
adjointable operators on $E_n$ which have smooth orbit under the canonical
action of the Heisenberg group. We construct a left inverse for $O$, $S:H\to
B$, and prove that $S$ is an inverse for $O$ if $C$ is commutative. The case
when $C$ is the complex numbers was proven by Cordes in 1979. As a consequence,
we prove, for commutative separable unital C*algebras, a characterization of a
certain class of pseudodifferential operators conjectured by Rieffel in 1993.
