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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Thompson’s theorem for $\mathrm {II}_1$ factors
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by Matthew Kennedy and Paul Skoufranis PDF
Trans. Amer. Math. Soc. 369 (2017), 1495-1511 Request permission

Abstract:

A theorem of Thompson provides a non-self-adjoint variant of the classical Schur-Horn theorem by characterizing the possible diagonal values of a matrix with given singular values. We prove an analogue of Thompson’s theorem for II$_1$ factors.
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Additional Information
  • Matthew Kennedy
  • Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada
  • MR Author ID: 836009
  • Email: mkennedy@math.carleton.ca
  • Paul Skoufranis
  • Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095
  • MR Author ID: 966934
  • Email: pskoufra@math.ucla.edu
  • Received by editor(s): January 29, 2015
  • Received by editor(s) in revised form: February 28, 2015
  • Published electronically: March 21, 2016
  • Additional Notes: The first author was partially supported by a research grant from NSERC (Canada).
    The second author was partially supported by a research grant from the NSF (USA)
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1495-1511
  • MSC (2010): Primary 46L10; Secondary 15A42
  • DOI: https://doi.org/10.1090/tran/6711
  • MathSciNet review: 3572280