  Let Q and P be the position and momentum operators of a particle in one
dimension. It is shown that all compact operators can be approximated in norm
by linear combinations of the basic resolvents (aQ + bP - i r)^{-1} for real
constants a,b,r=/=0. This implies that the basic resolvents form a total set
(norm dense span) in the C*-algebra R generated by the resolvents, termed
resolvent algebra. So the basic resolvents share this property with the unitary
Weyl operators, which span the Weyl algebra. These results obtain for finite
systems of particles in any number of dimensions. The resolvent algebra of
infinite systems (quantum fields), being the inductive limit of its finitely
generated subalgebras, is likewise spanned by its basic resolvents.
