## A “quantum” Ramsey theorem for operator systems

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- by Nik Weaver PDF
- 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 $k^2$.## References

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## Additional Information

**Nik Weaver**- Affiliation: Department of Mathematics, Washington University, Saint Louis, Missouri 63130
- MR Author ID: 311094
- Email: nweaver@math.wustl.edu
- 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
- © Copyright 2017 Nik Weaver, all rights reserved
- 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
- MathSciNet review: 3691979