The Grothendieck constant is strictly smaller than Krivine's bound

TL;DR

This paper establishes that the Grothendieck constant is strictly less than Krivine's bound, providing a new upper limit for this fundamental constant in functional analysis.

Contribution

The authors prove a new strict inequality showing that the Grothendieck constant is smaller than previously known bounds, refining our understanding of its value.

Findings

Grothendieck constant is strictly less than Krivine's bound

Provides a new upper bound for the Grothendieck constant

Refines the theoretical limits in functional analysis

Abstract

We prove that $K_G<\frac{\pi}{2\log(1+\sqrt{2})}$, where $K_G$ is the Grothendieck constant.