A Bourgain-Pisier construction for general Banach spaces

We prove that every Banach space, not necessarily separable, can be isometrically embedded into an L∞-space in a way that the corresponding quotient has the Radon-Nikodym and the Schur properties. As a consequence, we obtain L∞ spaces of arbitrary large densities with the Schur and the Radon-Nikodym properties. This extends the result by J. Bourgain and G. Pisier in (1983) [6] for separable spaces.