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arXiv · 2609.25462

Sharper Bounds for the Complex Grothendieck Constant

Steven Heilman·Chris Jones·Giulio Malavolta
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Abstract

We show that $1.4<K_G^{\mathbb{C}}<1.404898554746$, where $K_G^{\mathbb{C}}$ is the complex Grothendieck constant. The upper bound improves on Haagerup's bound of $1.40490913\ldots$ from 1987, and the lower bound improves on Davie's bound of $1.33807$ from 1984. The upper bound combines ideas from the real and noncommutative complex cases of Grothendieck's inequality.

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Steven Heilman, Chris Jones, Giulio Malavolta. 2026-09-21. Sharper Bounds for the Complex Grothendieck Constant. https://arxiv.org/abs/2609.25462

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