  Some consequences of promoting the object of noncommutativity ${\mathbf
\theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a
consistent algebra involving the enlarged set of canonical operators is
obtained, which permits us to construct theories that are dynamically invariant
under the action of the rotation group. In this framework it is also possible
to give dynamics to the noncommutativity operator sector, resulting in new
features.
