English

A "quantum" Ramsey theorem for operator systems

Operator Algebras 2016-01-14 v2 Combinatorics Functional Analysis Rings and Algebras Quantum Physics

Abstract

Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under the formation of Hermitian adjoints. We prove that if n is sufficiently large then there exists a rank k orthogonal projection P such that dim(PVP) = 1 or k^2.

Keywords

Cite

@article{arxiv.1601.01259,
  title  = {A "quantum" Ramsey theorem for operator systems},
  author = {Nik Weaver},
  journal= {arXiv preprint arXiv:1601.01259},
  year   = {2016}
}

Comments

11 pages; added a final section which includes a common generalization of the classical and quantum Ramsey theorems

R2 v1 2026-06-22T12:24:11.271Z