Sharper Bounds for the Complex Grothendieck Constant

2026-09-21

AI Summary

本文通过结合实数和非交换复数情况下的Grothendieck不等式思想，改进了复Grothendieck常数的上下界估计。

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.

Problem

• Grothendieck Constant
• Complex Number
• Bounds

Innovation

• complex Grothendieck constant
• Sharper bounds
• noncommutative complex cases