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Transactions of the American Mathematical Society

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Thompson's theorem for $ II_1$ factors


Authors: Matthew Kennedy and Paul Skoufranis
Journal: Trans. Amer. Math. Soc. 369 (2017), 1495-1511
MSC (2010): Primary 46L10; Secondary 15A42
DOI: https://doi.org/10.1090/tran/6711
Published electronically: March 21, 2016
MathSciNet review: 3572280
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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
Email: mkennedy@math.carleton.ca

Paul Skoufranis
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095
Email: pskoufra@math.ucla.edu

DOI: https://doi.org/10.1090/tran/6711
Keywords: Schur-Horn, Thompson, von Neumann algebra, MASA, singular values, eigenvalues, diagonal, conditional expectation
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)
Article copyright: © Copyright 2016 American Mathematical Society

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