Sharper Bounds for the Complex Grothendieck Constant

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.

Functional Analysis (math.FA); Data Structures and Algorithms (cs.DS); Quantum Physics (quant-ph)

arXiv:2609.25462 [math.FA]

(or arXiv:2609.25462v1 [math.FA] for this version)

https://doi.org/10.48550/arXiv.2609.25462 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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