New proofs of Rosenthal's ℓ¹--theorem and the Josefson--Nissenzweig theorem

1994/03/31 by Ehrhard Behrends, Behrends, Ehrhard · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.math/9403211

Abstract

We give elementary proofs of the theorems mentioned in the title. Our methods rely on a simple version of Ramsey theory and a martingale difference lemma. They also provide quantitative results: if a Banach space contains ℓ¹ only with a bad constant then every bounded sequence admits a subsequence which is ``nearly'' a weak Cauchy sequence.

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• Quantitative Schur property and measures of weak non-compactness

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