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PreprintarXiv licencearXiv

Sharper Bounds for the Complex Grothendieck Constant

  • Steven Heilman
  • Chris Jones
  • Giulio Malavolta
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Abstract

We show that 1.4<KGℂ<1.404898554746, where KGℂ is the complex Grothendieck constant. The upper bound improves on Haagerup's bound of 1.40490913… 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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Cite

BibTeXRIS
BibTeX
@misc{heilman2026sharper,
  title = {{Sharper Bounds for the Complex Grothendieck Constant}},
  author = {Steven Heilman and Chris Jones and Giulio Malavolta},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25462},
  eprint = {2609.25462},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25462},
}
RIS
TY  - UNPB
TI  - Sharper Bounds for the Complex Grothendieck Constant
AU  - Steven Heilman
AU  - Chris Jones
AU  - Giulio Malavolta
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25462
UR  - https://arxiv.org/abs/2609.25462
AB  - We show that 1.4<K_G^ℂ<1.404898554746, where K_G^ℂ is the complex Grothendieck constant. The upper bound improves on Haagerup's bound of 1.40490913… 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.
ER  -