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Proceedings of the American Mathematical Society

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A ``quantum'' Ramsey theorem for operator systems


Author: Nik Weaver
Journal: Proc. Amer. Math. Soc. 145 (2017), 4595-4605
MSC (2010): Primary 05C55, 05D10, 13C99, 15A60, 46L07
DOI: https://doi.org/10.1090/proc/13606
Published electronically: May 26, 2017
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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 $ {\rm dim}(P\mathcal {V}P) = 1$ or $ k^2$.


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Additional Information

Nik Weaver
Affiliation: Department of Mathematics, Washington University, Saint Louis, Missouri 63130
Email: nweaver@math.wustl.edu

DOI: https://doi.org/10.1090/proc/13606
Received by editor(s): July 28, 2016
Received by editor(s) in revised form: November 26, 2016
Published electronically: May 26, 2017
Additional Notes: Part of this work was done at a workshop on Zero-error information, Operators, and Graphs at the Universitat Autònoma de Barcelona
Communicated by: Adrian Ioana
Article copyright: © Copyright 2017 Nik Weaver, all rights reserved