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arXiv · 1210.5728

A Bourgain-Pisier construction for general Banach spaces

J. Lopez-Abad
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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.

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J. Lopez-Abad. 2012-10-21. A Bourgain-Pisier construction for general Banach spaces. https://arxiv.org/abs/1210.5728

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