  We investigate a scale of dyadic operator-valued BMO spaces, corresponding to
the different yet equivalent characterizations of dyadic BMO in the scalar
case. In the language of operator spaces, we investigate different operator
space structures on the scalar dyadic BMO space which arise naturally from the
different characterisations of scalar BMO. We also give sharp dimensional
growth estimates for the sweep of functions and its bilinear extension in some
of those different dyadic BMO spaces.
