A “quantum” Ramsey theorem for operator systems

Weaver, Nik

doi:10.1090/proc/13606

A “quantum” Ramsey theorem for operator systems
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Proc. Amer. Math. Soc. 145 (2017), 4595-4605

Abstract:

Let $\mathcal {V}$ be a linear subspace of $M_n(\mathbb {C})$ 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 $\textrm {dim}(P\mathcal {V}P) = 1$ or $k^2$.

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