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Corpus ID: 119136054

An infinite quantum Ramsey theorem

@article{Kennedy2017AnIQ,
title={An infinite quantum Ramsey theorem},
author={Matthew G. Kennedy and Taras Kolomatski and D. Spivak},
journal={arXiv: Operator Algebras},
year={2017}
}

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.