A Bourgain-Pisier construction for general Banach spaces

2012/10/21 by J. López-Abad, Lopez-Abad, J.
Mathematics · #46B03 #46B26 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1210.5728

openalex publication_date 2012/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every Banach space, not necessarily separable, can be isometrically embedded into a \mathcal L_∞-space in a way that the corresponding quotient has the Radon-Nikodym and the Schur properties. As a consequence, we obtain \mathcal L_∞ 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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