The Grothendieck constant is strictly smaller than Krivine's bound

Mark Braverman; Konstantin Makarychev; Yury Makarychev; Assaf Naor

The Grothendieck constant is strictly smaller than Krivine's bound

Functional Analysis 2011-08-18 v3 Data Structures and Algorithms

Authors: Mark Braverman , Konstantin Makarychev , Yury Makarychev , Assaf Naor

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Abstract

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

Keywords

grothendieck constant krivine bound inequality banach space operator theory

Cite

@article{arxiv.1103.6161,
  title  = {The Grothendieck constant is strictly smaller than Krivine's bound},
  author = {Mark Braverman and Konstantin Makarychev and Yury Makarychev and Assaf Naor},
  journal= {arXiv preprint arXiv:1103.6161},
  year   = {2011}
}