  The operator space analogue of the {\em strong form} of the principle of
local reflexivity is shown to hold for any von Neumann algebra predual, and
thus for any $C^{*}$-algebraic dual. This is in striking contrast to the
situation for $C^{*}$-algebras, since, for example, $K(H)$ does not have that
property. The proof uses the Kaplansky density theorem together with a careful
analysis of two notions of integrality for mappings of operator spaces.
