  We work with functions defined in R^n with values in a C^*- algebra A. We
consider the set \Sa of the functions of Schwartz (the rapidly decreasing ones)
with the usual l_2-norm. We denote \CB^{2n}A the set of functions of class
C^\infty with bounded derivatives. We prove, generalizing a result in [10],
that pseudodifferential operators with symbol in \CB^{2n}A are continuous in
\Sa for the l_2-norm. In[1], Rieffel proves that \CB^nA acts on \Sa, through a
deformed product induced by an anti-symmetric matrix, J (this is the so-called
left-regular representation of \CB^{2n}A).
  At the end of chapter 4, Rieffel poses the conjecture that all operators
adjointable in \Sa and that commute with the right-regular representation of
\CB^nA (for the deformed product above) are precisely the operators of the
left-regular representation. We prove this for the case A=C (the complex
numbers)(see [14]), using Cordes characterization of Heisenberg-smooth
operators on L^2(R^n) as the pseudodifferential operators with symbol in
\CB^{2n}C (see [17]). We also prove in this work that, if the natural
generalization of Cordes characterization holds, then Rieffel's conjecture also
holds.
