This is an announcement for the paper "A Bourgain-Pisier construction for general Banach spaces" by J. Lopez-Abad.

Abstract: We prove that every Banach space, not necessarily separable, can be isometrically embedded into a $\mathcal L_{\infty}$-space in a way that the corresponding quotient has the Radon-Nikodym and the Schur properties. As a consequence, we obtain $\mathcal L_\infty$ spaces of arbitrary large densities with the Schur and the Radon-Nikodym properties. This extents the a classical result by J. Bourgain and G. Pisier.

Archive classification: math.FA

Mathematics Subject Classification: 46B03, 46B26

Submitted from: abad@icmat.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1210.5728

or

http://arXiv.org/abs/1210.5728