  Using fast confocal microscopy we image the three-dimensional dynamics of
particles in a yielded hard-sphere colloidal glass under steady shear. The
structural relaxation, observed in regions with uniform shear, is nearly
isotropic but is distinctly different from that of quiescent metastable
colloidal fluids. The inverse relaxation time $\tau_\alpha^{-1}$ and diffusion
constant $D$, as functions of the {\it local} shear rate $\dot{\gamma}$, show
marked shear thinning with $\tau_\alpha^{-1} \propto D \propto
\dot{\gamma}^{0.8}$ over more than two decades in $\dot{\gamma}$. In contrast,
the {\it global} rheology of the system displays Herschel-Bulkley behavior. We
discuss the possible role of large scale shear localization and other
mechanisms in generating this difference.
