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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $k^2$.
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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