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.
Categories: math.OA math.FA