An infinite quantum Ramsey theorem
Operator Algebras
2017-11-28 v1 Mathematical Physics
Combinatorics
Functional Analysis
math.MP
Abstract
We prove an infinite Ramsey theorem for noncommutative graphs realized as unital self-adjoint subspaces of linear operators acting on an infinite dimensional Hilbert space. Specifically, we prove that if V is such a subspace, then provided there is no obvious obstruction, there is an infinite rank projection P with the property that the compression PVP is either maximal or minimal in a certain natural sense.
Cite
@article{arxiv.1711.09526,
title = {An infinite quantum Ramsey theorem},
author = {Matthew Kennedy and Taras Kolomatski and Daniel Spivak},
journal= {arXiv preprint arXiv:1711.09526},
year = {2017}
}
Comments
19 pages