Integral mappings and the principle of local reflexivity for noncommutative L¹-spaces

The operator space analogue of the 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.