REAL BANACH SPACES WITH NUMERICAL INDEX 1

GINÉS LÓPEZ; MIGUEL MARTÍN; RAFAEL PAYÁ

doi:10.1112/S002460939800513X

Abstract

We show that an infinite-dimensional real Banach space with numerical index 1 satisfying the Radon–Nikodym property contains l1. It follows that a reflexive or quasi-reflexive real Banach space cannot be re-normed to have numerical index 1, unless it is finite-dimensional.

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CrossRef

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REAL BANACH SPACES WITH NUMERICAL INDEX 1

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