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arXiv · 1711.10595

An elementary and unified proof of Grothendieck's inequality

Shmuel Friedland·Lek-Heng Lim·Jinjie Zhang
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Abstract

We present an elementary, self-contained proof of Grothendieck's inequality that unifies the real and complex cases and yields both the Krivine and Haagerup bounds, the current best-known explicit bounds for the real and complex Grothendieck constants respectively. This article is intended to be pedagogical, combining and streamlining known ideas of Lindenstrauss--Pe{\l}czy\'nski, Krivine, and Haagerup into a proof that need only univariate calculus, basic complex variables, and a modicum of linear algebra as prerequisites.

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Shmuel Friedland, Lek-Heng Lim, Jinjie Zhang. 2017-11-28. An elementary and unified proof of Grothendieck's inequality. https://arxiv.org/abs/1711.10595

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