  We consider Holder continuous cocycles over hyperbolic dynamical systems with
values in the group of invertible bounded linear operators on a Banach space.
We show that two fiber bunched cocycles are Holder continuously cohomologous if
and only if they have Holder conjugate periodic data. The fiber bunching
condition means that non-conformality of the cocycle is dominated by the
expansion and contraction in the base system. We show that this condition can
be established based on the periodic data of a cocycle. We also establish
Holder continuity of a measurable conjugacy between a fiber bunched cocycle and
one with values in a set which is compact in strong operator topology.
