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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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On the distinction between the classes of Dixmier and Connes-Dixmier traces
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by Fedor Sukochev, Alexandr Usachev and Dmitriy Zanin PDF
Proc. Amer. Math. Soc. 141 (2013), 2169-2179 Request permission

Abstract:

We prove that the classes of Dixmier and Connes-Dixmier traces differ even on the Dixmier ideal $\mathcal M_{1,\infty }$. We construct a Marcinkiewicz space $\mathcal M_\psi$ and a positive operator $T\in \mathcal M_\psi$ which is Connes-Dixmier measurable but which is not Dixmier measurable.
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Additional Information
  • Fedor Sukochev
  • Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
  • MR Author ID: 229620
  • Email: f.sukochev@unsw.edu.au
  • Alexandr Usachev
  • Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
  • Email: a.usachev@unsw.edu.au
  • Dmitriy Zanin
  • Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
  • MR Author ID: 752894
  • Email: d.zanin@unsw.edu.au
  • Received by editor(s): September 22, 2011
  • Published electronically: December 28, 2012
  • Additional Notes: The authors’ research was supported by the Australian Research Council
  • Communicated by: Varghese Mathai
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2169-2179
  • MSC (2010): Primary 58B34, 46L52
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11853-2
  • MathSciNet review: 3034443