English

Column bounded matrices and Grothendieck's inequalities

Functional Analysis 2025-05-09 v1 Mathematical Physics math.MP Operator Algebras Quantum Algebra

Abstract

It follows from Grothendieck's little inequality that to any complex (m x n) matrix X of column norm at most 1, and an 0 <e <1, there exist a natural number q, an (m x q) matrix C with (1e)2CC(4/π)(1+e)2(1-e)^2 \leq CC^* \leq (4/\pi) (1 + e)^2 and an (q x n ) matrix Z with entries in the complex torus such that X= q(1/2)^{-(1/2)}(CZ). Both of Grothendieck's complex inequalities follow from this factorization result.

Keywords

Cite

@article{arxiv.2505.04545,
  title  = {Column bounded matrices and Grothendieck's inequalities},
  author = {Erik Christensen},
  journal= {arXiv preprint arXiv:2505.04545},
  year   = {2025}
}
R2 v1 2026-06-28T23:24:41.121Z